Talk:Centrifugal force/Archive 9

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Last paragraph of the introduction

You ignored my comment about the paragraph you added to the introduction. Your text was about a very important point, and in my opinion its content was very useful, and I am glad you proposed to add it to the article. However, if you compare your text with the version I edited a few minutes ago, you will immediately understand how many sentences in that paragraph were sloppily written and how many logic steps (which I am sure for you were obvious) were not explained to the reader. A clear conclusion was also missing. You edited an A class article, and your text looked like a quick comment by an unexperienced writer on a talk page. You repeatedly showed that you can do much better. So, I assume you were in a hurry. Please do not edit articles (especially highly rated articles) when you are in a hurry, and please do not ignore what I write.

By the way, I think this article, as it is now, is too badly structured to deserve the A class. Paolo.dL (talk) 11:50, 13 July 2008 (UTC)

I know that I've been out of the loop on the editing for awhile here, and have only made it part way through the discussions for the past month. However, it appears to me that there is an error in the last paragraph of the introduction. It states, "Let L be a local and non-inertial reference frame the origin of which is attached to the particle", which I take to mean that the particle is always at the origin of L. First question, is that the meaning of this statement? If this is true, then the centrifugal force in frame L acting on the particle is always zero since the position vector is always zero. Just as the zero velocity vector in L kills the Coriolis force, a zero position vector in L kills the centrifugal force in that frame, which leaves the only fictitious force as that associated with the acceleration of the origin of L in the inertial frame (the first term in the general derivation of the fictitious force at the end of Fictitious force#General derivation). Now, am I missing something? Or have we in our attempts to present a situation where the Coriolis force term is zero, inadvertantly also killed the centrifugal force term. --FyzixFighter (talk) 14:08, 13 July 2008 (UTC)

I am sorry, I wrote that sentence and I am not a native speaker. Can you explain what else might the expression "attached to the particle" mean? I thought it was exactly and unambiguously equivalent to (but less formal than) "coinciding with the particle". The paragraph is correct, and actually points out how simplified versions of the definition formula of the centrifugal force, that we sometimes use in special cases, are not valid in the general case: centrifugal force is not zero in this case, because the axis of rotation does not coincide with the origin of L. Paolo.dL (talk) 14:51, 13 July 2008 (UTC)

This paragraph is really bad: it is redundant, it is unclear, it is over detailed and it is unnecessary. In short, it is not an improvement. I have removed it. Brews ohare (talk) 15:50, 13 July 2008 (UTC)

I have moved the discussion of local coordinates to Centrifugal_force#Moving_objects_and_frames_of_reference, where there is enough room to discuss it. Brews ohare (talk) 16:33, 13 July 2008 (UTC)

This paragraph was inserted by you in the introduction! I asked you to make it clearer. Since you ignored my request, I just made it clearer in all respects, and added a clear conclusion which in your version was missing, as the following comparison shows. Moreover, in my edit summary I wrote that it did "not necessarily belong in the introduction". Now you rewrote it in another section, and completely ignored my work. You behave as if you were the owner of the page.

Brews ohara	Paolo.dL
In a frame that rotates about a fixed axis, ...	In a frame that rotates about a fixed axis, ...
In non-inertial reference frames that are more complex than rotation about a fixed axis, the fictitious forces take on different behaviors. (For a discussion of more complex rotations, see Euler angles.)	When the reference frame rotates about an axis which is not fixed, the fictitious forces take on a more complex behavior. (For a discussion of complex rotations, see Euler angles.)
As a simple example of different behavior, consider general planar motion of a particle along a curvilinear path.	As a simple example, consider general planar motion of a particle at constant speed along a snake-shaped path (that is, a curvilinear but not circular planar path).
	Let L be a local and non-inertial reference frame the origin of which is attached to the particle, and which rotates to keep its xL and yL axes always perpendicular and tangent to the trajectory of the particle (see local coordinates). Namely, if we observe L from an inertial frame, we see that the direction of xL and yL varies as the particle position changes, approximately as if L (and the particle) were attached to a tiny train truck running along a very narrow railway having the same shape as the particle trajectory.
In the reference frame of the moving particle (see local coordinates) the centrifugal force acts outward along the radius of curvature of the path at each position on the path. It therefore varies in direction as the trajectory changes to remain continuously normal to the path.	In frame L, the centrifugal force applied on the particle acts outward from the centre of curvature of the path at each particle position. It therefore remains continuously perpendicular to the path, i.e. parallel to xL.
	[CONCLUSION] However, the magnitude and even the sense of the centrifugal force vary with time (e.g., when the curvature is to the left, the centrifugal force has the same direction as xL, while when the curvature is to the right the centrifugal force points in the opposite direction). Thus, the centrifugal force is time-variant even though the mass and the position in L of the particle are both time-invariant. This means that, when L rotates about a non-fixed axis, the centrifugal force ceases to be a simple function of mass and position, and becomes a more complex function.
The Coriolis force is zero in this reference frame, because the frame is attached to the moving particle, and therefore the particle has zero velocity in this frame. (However, another object viewed from this frame can be subject to Coriolis force if it has a velocity as seen in this frame.)	Notice that the Coriolis force acting on the particle is zero in L, because the particle has zero velocity in this frame.

Aren't there policies in Wikipedia against this kind of behaviour? Paolo.dL (talk) 17:17, 13 July 2008 (UTC)

Hi Paolo:

Sorry to cause so much excitement. I believe my changes are appropriate, and provide a clear discussion of the situation in an appropriate setting. I do not see any need for the changes you outline above.

It may be that I'm a bit high-handed in changing this page. I have contributed all the examples, all but one of the figures, and most of the discussion. I also rated the page Class A. That may have led to a proprietary viewpoint on my part. Brews ohare (talk) 17:34, 13 July 2008 (UTC)

Even if you were the author of every single word in this article, this would not excuse you. I value your work and pictures, but you should respect the work of others, and you cannot write on this talk page that the paragraph was not clear and not good for the introduction, when (1) you put it in the introduction and (2) my revision was much clearer than yours. And more importantly, you cannot rewrite from scratch a text that you inserted yourself, just because somebody else edited it. Imagine what would happen if others did the same with your work. Paolo.dL (talk) 17:49, 13 July 2008 (UTC)

Hi Paolo:

Of course, I agree about editing responsibility. I do believe my discussion in Centrifugal_force#Moving_objects_and_frames_of_reference is responsive to your concerns. Brews ohare (talk) 17:58, 13 July 2008 (UTC)

It does not address my concern because you rewrote it from scratch. Paolo.dL (talk) 18:11, 13 July 2008 (UTC)

Fictitious forces in general case

At present the article states "the centrifugal force does not depend only on the mass and position of the object". This remark could be made more helpful. There is no suggestion as to what the other dependencies might be, and no reference to further discussion. In the case of general curvilinear particle motion using a local coordinate system, the statement is incorrect. I have seen no discussion for a general rigid body, so I do not know if it is a correct statement in that case. (it seems very likely to be true, because the orientation angles must enter.) I wonder if any references could be provided? Brews ohare (talk) 18:38, 13 July 2008 (UTC)

You mean that the centrifugal force is zero, in the above mentioned example (particle motion using a local coordinate system)? You mean it is not equal and opposite to the real centripetal force in this case? (you might be right, I am not sure). Why didn't you write this in your edit summary? Brews, let's discuss this briefly before you make the introduction unnecessarily more complex (the introduction is now much better focused and structured than it was before). If you don't mind, I will remove (at least temporarily) my statement, because I am not anymore sure it is correct. Paolo.dL (talk) 19:05, 13 July 2008 (UTC)

About your edit: Newton-Euler equations for linear motion treat the rigid body as if it were a particle at its center of mass. The angular version is about body rotation, not ref frame rotation. So, it is not clear to me what you mean. Paolo.dL (talk) 19:15, 13 July 2008 (UTC)

Paolo: The centrifugal force does not vanish. You could answer your questions by looking at the modified section on local coordinates and looking at the link to the book referenced. (The relevant portion is on-line at googlebooks at the link). Brews ohare (talk) 19:25, 13 July 2008 (UTC)

Brews: your new section was not clear and contained mistakes (which I partly corrected). You were wrong when you wrote that the local coordinate system is inertial. You were also wrong when you wrote that the normal force (in this frame) is centripetal. The net normal force and the net tangential force must be both null in this frame, because the acceleration of the particle is null in it. So, there must exist some other fictitious force which counteracts the real centripetal force, otherwise the equations of motion would not work. Now, I thought that this additional fictitious force, equal and opposite to centripetal, was the centrifugal force, but now I am not sure anymore. It could be reagarded as another kind of force (D'Alembert force?) associated with the linear acceleration of the origin (and in this case it does not matter if the acceleration is centripetal or it has a constant or variable magnitude or direction or whatever)! It depends on how you define centrifugal force in the general case. You define it as a function of the distance from the center of curvature (which does not coincide with origin), or always as a function of the distance from the origin? Do you understand now my doubt? Paolo.dL (talk) 19:48, 13 July 2008 (UTC)

Hi Poalo: I haven't time just now to look at this matter carefully, as I have an appointment. However, there are two coordinate systems involved, and the particle is at rest only in one of the two. The normal force is centripetal in the frame where the particle moves. The motion there is observed as instantaneously circular with a radius given by the osculating circle. Brews ohare (talk) 20:08, 13 July 2008 (UTC)

Well, there are three frames in your example. The inertial frame, and the two non-inertial (rotating) frames. For sure, in the two rotating frames, we do not see only a centripetal force. (And yes, of course, only in one of them the particle is motionless). Paolo.dL (talk) 20:22, 13 July 2008 (UTC)

I have rewritten this section with the unfortunate necessity of including already presented material from Fictitious forces, which seems to be required to get the point across. Brews ohare (talk) 03:40, 14 July 2008 (UTC)

It seems likely that some discussion has to appear somewhere (maybe in another article altogether) relating frames of reference and coordinate systems. The first describes the mechanical state of motion of the frame. In any frame, any coordinate system may be used as a language to describe what is observed: Cartesian, polar, elliptical, etc. In particular, a local coordinate system can be used in both an inertial and in a non-inertial frame. In the inertial frame of this article, the unit vectors of the local system are not fixed in orientation, but rotate as the particle moves. In a non-inertial frame tied to the moving particle, the orientation of these same unit vectors are fixed in time. Brews ohare (talk) 12:54, 14 July 2008 (UTC)

Maybe the article is clearer now for an uninitiated reader. That is the hope of Wikipedia's free-for-all editing process, I'd guess. Brews ohare (talk) 13:22, 14 July 2008 (UTC)

A simplified example on which we all should agree

Here's the simplest possible example in which I am not sure anymore about the correct definition of the centrifugal force: a reference frame which is rotating at constant angular velocity about a fixed axis which does not coincide with its origin. For instance, a local frame attached to a car moving along a circular path, with its origin sitting at the center of mass of the car driver, not at the center of the circular path. The driver is at rest in this frame (null linear and angular velocity and null linear and angular acceleration), thus the net force (fictitious+real) must be zero. Questions:

1. Obviously, there must be a fictitious force (equal and opposite to centripetal) acting on the driver. But can we call it "centrifugal force" in this case?
2. Or should we call it with a different name? (if yes, what name)?

Paolo.dL (talk) 20:22, 13 July 2008 (UTC)

Paolo: Please look at Centripetal_force#Alternative_approach for a presentation at variance with your ideas. Brews ohare (talk) 20:24, 13 July 2008 (UTC)

I have not clear ideas about this (although I have a best guess). My doubt is about the correct definition of centrifugal force in the gereral case. But my example is extremely simple. Can you all give me your opinion? I believe it is important. Whatever is the correct answer, changes must be made in the article accordingly. Thanks. Paolo.dL (talk) 20:42, 13 July 2008 (UTC)

Just do a coordination translation to everything in the eccentric frame so that the origin now rests on the rotation axis. Since a translation doesn't change any accelerations you have now created the same situation as the article covers. So in this case, the driver is subject to a centripetal and centrifugal force and it behaves exactly as you would expect.- (User) WolfKeeper (Talk) 22:53, 13 July 2008 (UTC)

Is it possible that this example is similar to Fictitious_force#Orbiting_and_rotating? Maybe it's time to do some math, eh? And maybe to study the relevant articles? Brews ohare (talk) 01:29, 14 July 2008 (UTC)

There's no need to resort to mathematics. You just need to think about what is happening to the reference frame. It is rotating, therefore there is a centrifugal force. It is also accelerating, therefore there is a fictitious force due to that. The sum of these must be equal and opposite to the real force.

On the issue of "studying the relevant articles" it should be pointed out that a Wikipedia article can be edited by anyone, and therefore cannot be used as an argument in a discussion. The section Fictitious_force#Orbiting_and_rotating contains no reference to reliable sources, and can therefore be considered original research. Editors should not be expected to read all the OR on Wikipedia before participating in discussions. --PeR (talk) 06:59, 15 July 2008 (UTC)

Technically an accurate statement. However, I do not believe there is any dispute over the accuracy of Fictitious_force#Orbiting_and_rotating, only a lack of awareness that it is already out there and answers the questions posed by Paolo about this example on this talk page. Brews ohare (talk) 13:28, 15 July 2008 (UTC)

Regarding the use of nested frames of reference. This is a mathematical curiosity that has no place in this article i.m.o. Of course you can see the car as a rotating frame of reference where the origin is stationary in another rotating frame of reference, and therefore call both of the above mentioned fictitious forces "centrifugal". However, that makes things gratuitously complex, and does not provide any additional information about the subject of the article, namely the Centrifugal force.

If someone wants to write an article on nested frames of reference, that's fine, of course. But for this article, let's make everything as simple as possible (but not simpler!) --PeR (talk) 08:50, 15 July 2008 (UTC)

Call the topic Fictitious_force#Orbiting_and_rotating a "mathematical curiosity" if you wish, but as the article Fictitious_force#Orbiting_and_rotating points out, it is relevant to the centrifuge, not exactly a rare or obscure application of centrifugal force. Brews ohare (talk) 13:28, 15 July 2008 (UTC)

It is perfectly feasible to do calculations for a centrifuge while placing the origin at the center of rotation, and for the purposes of explaining what a centrifugal force is, that wold seem to be the simplest way. (Just set $\mathbf {X} _{AB}=0$ in the above-mentioned example, and see how much simpler the equations become.) There might be a reason to have the origin move with the test tube in some particular application, but then I think it would be a good idea to cite a source that does the calculation that way. --PeR (talk) 14:21, 15 July 2008 (UTC)

Just to clarify again. I'm not saying that it is "wrong" to do the calculations one way instead of the other. My point is rather that Wikipedia is an encyclopedia, not a textbook, and as such it should be providing facts with references, not mathematical deductions. --PeR (talk) 14:42, 15 July 2008 (UTC)

Brews suggested "maybe it's time to do some math, eh?". My suggestion is to read with more attention before answering (it would enormously facilitate our discussions). My questions were extremely clear and simple: this is just a matter of terminology. Nobody doubts that a fictitious force exists in this case and everybody knows how to compute it!

Anyway, I am glad that WolfKeeper, Brews, PeR and Wikipedia (as Brews pointed out) agree to call this fictitious force "centrifugal force". This supports my initial thesis. FyzixFighter wrote above (14:08 13 July 2008): "the centrifugal force in frame L acting on the particle is always zero since the position vector is always zero", but he probably changed his mind after reading my answer (14:51, 13 July 2008). If someone still disagrees, please let us know as soon as possible. I would love to be able to write again: "agreement reached". (not ignoring PeR's interesting point; I will discuss it later). Paolo.dL (talk) 18:11, 15 July 2008 (UTC)

I didn't mean to say that you should call the fictitious force "centrifugal force". Nor did WoolfKeeper, as far as I can see. What we both said is that if you move the origin to the center of rotation, then the fictitious force is the centrifugal force. As you formulated the example there are two fictitious forces involved. One is the centrifugal force, and the other is discussed in the section here below. Their sum is equal and opposite to the real force.

Update: I just read your example more carefully. The object in question is at the origin. In this case I agree with FyzixFighter. The centrifugal force is zero. What is left is the fictitious force due to the acceleration of the reference frame, as discussed below. The simple solution seems to be to get rid of the superfluous reference frame. (Why introduce a reference frame where you only use the origin?) --PeR (talk) 21:56, 15 July 2008 (UTC)

Orbiting coordinate systems

Figure 3: An orbiting but fixed orientation coordinate system B, shown at three different times. The unit vectors u_j, j = 1, 2, 3 do not rotate, but maintain a fixed orientation, while the origin of the coordinate system B moves at constant angular rate ω about the fixed axis Ω. Axis Ω passes through the origin of inertial frame A, so the origin of frame B is a fixed distance R from the origin of inertial frame A.

As a related example, suppose the moving coordinate system B rotates in a circle of radius R about the fixed origin of inertial frame A, but maintains its coordinate axes fixed in orientation, as in Figure 3. The acceleration of an observed body is now:

${\frac {d^{2}\mathbf {x} _{A}}{dt^{2}}}=\mathbf {a} _{AB}+\mathbf {a} _{B}$ $+2\ \sum _{j=1}^{3}v_{j}\ {\frac {d\mathbf {u} _{j}}{dt}}$ $+\sum _{j=1}^{3}x_{j}\ {\frac {d^{2}\mathbf {u} _{j}}{dt^{2}}}\ .$

$=\mathbf {a} _{AB}\ +\mathbf {a} _{B}\ ,$

where the summations are zero inasmuch as the unit vectors have no time dependence. The origin of system B is located according to frame A at:

$\mathbf {X} _{AB}=R\left(\cos(\omega t),\ \sin(\omega t)\right)\ ,$

leading to a velocity of the origin of frame B as:

$\mathbf {v} _{AB}={\frac {d}{dt}}\mathbf {X} _{AB}=\mathbf {\Omega \times X} _{AB}\ ,$

leading to an acceleration of the origin of B given by:

$\mathbf {a} _{AB}={\frac {d^{2}}{dt^{2}}}\mathbf {X} _{AB}$ $=\mathbf {\Omega \ \times } \left(\mathbf {\Omega \times X} _{AB}\right)$ $=-\omega ^{2}\mathbf {X} _{AB}\ .$

The observers in frame B therefore must introduce a fictitious force, this time due to the acceleration from the orbital motion of their entire coordinate frame, that is radially outward away from the center of rotation of the origin of their coordinate system:

$\mathbf {F} _{\mathrm {fict} }=m\omega ^{2}\mathbf {X} _{AB}\ ,$

and of magnitude:

$|\mathbf {F} _{\mathrm {fict} }|=m\omega ^{2}R\ .$

Notice that this force is a centrifugal force, but has differences from the case of a rotating frame. In the rotating frame the centrifugal force is related to the distance of the object from the origin of frame B, while in the case of an orbiting frame, the centrifugal force is independent of the distance of the object from the origin of frame B, but instead depends upon the distance of the origin of frame B from its center of rotation, resulting in the same centrifugal fictitious force for all objects observed in frame B. Brews ohare (talk) 19:48, 15 July 2008 (UTC)

For those who don't know, this is a copy of a section of Fictitious force. Very interesting stuff. Particulary the last sentence, in which you can see that the "centrifugal" force field in the orbiting frame is uniform, rather than radial! Calling this force "centrifugal" is a convention. Actually, as I wrote privately to WolfKeeper (see his talk page), this example very well highlights how arbitrary our convention is. This is, however, perfectly consistent with what we discussed in the previous subsection. Again, I remind you that I am glad we all agree about this convention. Paolo.dL (talk) 20:51, 15 July 2008 (UTC)

Agreed. I don't think it's a good idea to call this force "centrifugal" in the article. That term is typically used for forces that are directed away from the center of rotation. As pointed out above, this force is independent of where the object is located, and that may well be in the opposite direction. (Semantically, I suppose that even if it is ambiguous at best to say that "the object experiences a centrifugal force" one could perhaps say that "the reference frame experiences a centrifugal force", but then we're back to nested reference frames, and as I said before, simpler is better.) Unless someone can come up with a reliable source that supports the current wording (The section is currently completely devoid of references.) I propose that the section be substantially rewritten, or removed. It would also be a good idea to move this whole discussion thread over to Talk: Fictitious force. --PeR (talk) 21:31, 15 July 2008 (UTC)

Calling the force "centrifugal" is a natural use of the term because it is of the form

$\mathbf {\Omega \ \times } \left(\mathbf {\Omega \times X} _{AB}\right)\ ,$

which is the same form as the normal centrifugal force expression:

${\boldsymbol {\Omega }}\times \left({\boldsymbol {\Omega }}\times \mathbf {x} _{B}\right)\ .$

Moreover, this term is simply the centrifugal force seen by a particle located at the origin of the orbiting coordinate system and rotating about the same axis as the orbiting frame. So I don't see much to doubt here. Brews ohare (talk) 22:26, 15 July 2008 (UTC)

Whether or not it's natural, I don't think that calling the frame acceleration of a circularly moving origin 'centrifugal' is standard terminology, but I'll certainly bow to a reliable source that says otherwise.- (User) WolfKeeper (Talk) 02:02, 16 July 2008 (UTC)

Great! This result is nothing more than substituting the derivative of a constant is zero into the general result. Go ahead and remove it. Brews ohare (talk) 02:26, 16 July 2008 (UTC)

I have revised this section so it is entirely in accord with all this nitpicking. Brews ohare (talk) 12:42, 16 July 2008 (UTC)

Car along S-shaped path (rotation about a non-fixed axis)

PeR, I thought your position was neutral, as mine. But now I see you express a preference against the convention currently adopted by Wikipedia (which, I agree, is not a reliable source). My example (rotation about fixed axis) was simplified, Brew's example (translation about fixed axis) was even more simplified, but the real subject of this discussion was rotation about a non-fixed axis (e.g. a car along an S-shaped planar path). Please think about that, and you will see a strong reason not to use a frame attached to the center of curvature: this is by no means equivalent to the frame from which the car driver observes the world. We have two non-inertial frames (both rotating at the same speed:

• one attached to the center of curvature (not local),
• the other to the driver's CM (local coordinate system, LCS)

These rotating frames are not equivalent, as for the observed position, velocity and acceleration of the car. They do accelerate relative to each other! In one of them, the car is of course at rest, but the center of curvature accelerates to the left or right, i.e. along the transverse axis of the car. In the other, you observe the opposite motion: the car accelerates to the right or left. This does not mean I disagree with you. Just that I find it hard to convince others that the imaginary force "experienced" by the car driver driving along an S-shaped trajectory is not centrifugal, in the driver's own natural frame of reference (i.e. his own LCS). This terminology does not seem to be based on math (math is neutral in this respect, in my opinion; you and Brews are both right about math); it seems to be also based on a philosophy and terminology which is meant to be intuitively appealing for laymen who don't have a good grasp of physics. Paolo.dL (talk) 23:31, 15 July 2008 (UTC)

The "car along S_shaped curve" could be a generalization from "particle along an S-shaped curve" to something more like "rigid body along an S-shaped curve". I'd suggest the easiest starting point is the example of "particle on an S-shaped planar curve". My view is that this example has been presented in exhausting detail in Centrifugal_force#Moving_objects_and_frames_of_reference. In terms of that presentation, what is missing? In particular, do you agree that the motion in the frame of the particle (the frame where the particle has zero velocity) sees the centrifugal force that is the opposite of the centripetal force of the osculating circle? Brews ohare (talk) 01:00, 16 July 2008 (UTC)

My position is "neutral" in the sense that I specified earlier. Namely: Wikipedia should not be setting the convention. I'm perfectly fine with statements such as "the driver of a car driving along an S-shaped path feels a centrifugal force pushing her towards the outside of each turn". This statement does not claim any mathematical rigor. It is adequate for a car driver who's aim is not to spill her coffee, but perhaps not for an engineer building a detailed model of the system.

However, when you do specify what coordinate system you are using, then you also need to take more care in labeling the fictitious forces. The term "centrifugal force" is typically reserved for the one that is due to the rotation of the coordinate system. Using the same label for a force that is due to acceleration of the origin is confusing at best, and I think it's plain wrong. But like WolfKeeper, I'll certainly bow to a reliable source that says otherwise. --PeR (talk) 08:13, 16 July 2008 (UTC)

Having thought some more: I believe there exists a frame of reference where you could say that "the driver of a car driving along a non-circular, curved path is subject to a centrifugal force that is equal and opposite to the sum of the real forces she experiences". In this frame, the origin moves so that it is always on the center of curvature, and the rate of rotation also changes. This gives rise to Coriolis, Euler, and other fictitious forces, and the driver is not stationary within this frame. I don't think anybody would want to use this frame, but because it exists it is mathematically correct to make statements like the ones I quote above where the frame is not specified. (For an S-shaped path, it becomes slightly more complex as the reference frame origin will move towards infinity on the straight part. Not impossible to handle, though.)

My point is, of course, that terms relating to fictitious forces are very imprecise unless you have specified the frame of reference. But "imprecise" is not the same as "wrong". I'm perfectly fine with both the imprecise and the precise-and-correct use of the term "centrifugal force". But I'm against precise-but-wrong use. --PeR (talk) 09:19, 16 July 2008 (UTC)

Outstanding contribution, PeR. Thank you for explaining so clearly your point. I conclude that we disagree about what is wrong. Of course nobody wants to use "precise-but-wrong" concepts. Brews's opinion is that you are wrong, my opinion is that both of you are right. I agree that the only way to solve the disagreement is to quote reliable literature. By the way, the rotating frame attached to center of curvature avoids the problem without solving it. And I agree with you: "nobody would want to use this frame". The very reason why I opened a new subsection was to discuss an example in which that frame becomes completely not natural and to give you a good reason to choose the driver's subjective frame (the LCS). Paolo.dL (talk) 10:10, 16 July 2008 (UTC)

It's nice that you and PeR agree with each other. However, your viewpoint is not correct. It is intuitively as well as analytically clear (as shown in exhaustive detail in the article) that a curved motion can be represented as a succession of arcs, and as stated in the article, for the limited time the radius of curvature is ρ, the forces can be analyzed as nonuniform circular motion with that radius. That is exactly how the discussion of airplane turns is handled, and a citation is provided to that effect. If you wish to challenge this analysis, please do so on some analytical basis, and not in a vague vocabulary. Please be clearer. Use some math. Provide some citations of your own. Brews ohare (talk) 12:20, 16 July 2008 (UTC)

Paolo:

I'll annotate your discussion below, repeating it line by line. Brews ohare (talk) 12:59, 16 July 2008 (UTC)

Part 1

|PeR, I thought your position was neutral, as mine. But now I see you express a preference against the convention currently adopted by Wikipedia (which, I agree, is not a reliable source). My example (rotation about fixed axis) was simplified, Brew's example (translation about fixed axis) was even more simplified, but the real subject of this discussion was rotation about a non-fixed axis (e.g. a car along an S-shaped planar path). Please think about that, and you will see a strong reason not to use a frame attached to the center of curvature: this is by no means equivalent to the frame from which the car driver observes the world. We have two non-inertial frames (both rotating at the same speed:

• one attached to the center of curvature (not local), ... (Paolo.dL 23:31, 15 July 2008 UTC)

This is partly correct; it is an instantaneous snapshot of the situation in the the initial inertial frame of reference. The term "local" in the article is meant to convey the choice of coordinates, not the frame of observation. Brews ohare (talk) 12:59, 16 July 2008 (UTC)

Why partly correct? "Instantaneous snapshot" means nothing. My comment deals with motion of reference frames and motion of their axes of rotation. I do not refer to instantaneous positions (i.e. snapshots). Your comment about the term local does not make sense to me. When you choose a coordinate system (Cartesian, polar, cilindrical, etc.), that represents your frame of reference. Paolo.dL (talk) 14:00, 16 July 2008 (UTC)

Paolo: Coordinate systems and frames of reference are independent: I can choose to describe a planetary orbit in elliptical coordinates or Cartesian, for example. They both can be referred to the fixed stars (inertial) or they could be fixed to the Sun (approximately inertial), or they could be fixed to the Moon (a wild choice and very non-inertial). More seriously, consider a wire fixed in space. The use of arc length to describe position on the wire in the inertial frame leaves the frame inertial. If now arc length is mapped to time, the frame is still inertial. Brews ohare (talk) 14:11, 16 July 2008 (UTC)

Your comment does not make sense to me. Do we agree that, if you choose a Cartesian coordinate system which rotates together with the moon, this is a non-inertial coordinate system and represents a non-inertial frame of reference? This frame of reference can be also represented by a polar coordinate system, or whatever, but chosing a coordinate system means chosing a reference frame. Do you agree? Paolo.dL (talk) 14:44, 16 July 2008 (UTC)

No, we do not agree. There are two separate issues:

1. What is our frame of reference? Are we at rest relative to the fixed stars or relative to the Moon, for example.
2. How do we wish to describe what we see? Is it simplest to use arc length, circular coordinates, or what ever. Should the coordinates relate to the path or relate to our origin?

My impression is that you would not care to imagine an observer on the Earth using a coordinate system centered on the Moon to describe a satellite orbiting the Moon. But that is feasible, and the Earth observer then will include effects due to the Moon orbiting the Earth that are omitted by a Moon observer using the same coordinate system to describe the satellite circling the Moon. Approximating the Earth as a frame more nearly an inertial frame than the Moon, the Moon observer will need to add fictitious forces. Brews ohare (talk) 14:59, 16 July 2008 (UTC)

Part 2

• the other to the driver's CM (local coordinate system, LCS). Paolo.dL (talk) 23:31, 15 July 2008 (UTC)

This is correct also, the particle is at rest in this frame; the coordinate system is the same as that in the inertial system. Brews ohare (talk) 12:59, 16 July 2008 (UTC)

Yes my sentence is correct, but yours is totally wrong. The coordinate system is rotating, hence not-inertial. The LCS as defined in my comment is totally different from both the other two coordinate systems (inertial and non-inertial non-local). I hope this is a typo. Paolo.dL (talk) 14:04, 16 July 2008 (UTC)

The coordinate system using arc length can be employed by any observer, inertial or non-inertial. See my previous comment. Brews ohare (talk) 14:15, 16 July 2008 (UTC)

Part 3

These rotating frames are not equivalent, as for the observed position, velocity and acceleration of the car. They do accelerate relative to each other! In one of them, the car is of course at rest, but the center of curvature accelerates to the left or right, i.e. along the transverse axis of the car. In the other, you observe the opposite motion: the car accelerates to the right or left. Paolo.dL (talk) 23:31, 15 July 2008 (UTC)

Of course, an inertial frame and a non-inertial frame are different, as you suggest. Your observation is not a source of controversy. Brews ohare (talk) 12:59, 16 July 2008 (UTC)

So your comment in previous subsection was not a typo. You totally misunderstood my example. We have been discussing it with PeR, you posted comments about it, and you still haven't read it with attention. I was comparing two different non-inertial frames! As I already wrote, if you read with more attention before answering, this would save us a lot of time and facilitate our discussions. Paolo.dL (talk) 14:12, 16 July 2008 (UTC)

Paolo: I feel you admonitions to be out of place. I am trying. I feel that your remarks express my feelings about your own inattention to my efforts. Brews ohare (talk) 14:16, 16 July 2008 (UTC)

I do not want to offend. I only would like to discuss about what we write, not about a distorted image of what we write. Do you agree that the subject of my sentence is "These rotating frames", and your answer is about the difference between an inertial and a non-inertial frame? Do you understand how much this is frustrating and time-consuming? Paolo.dL (talk) 14:50, 16 July 2008 (UTC)

Paolo: Yes, I agree. I've come to realize that this frustration is a consequence of this form of communication. It is so narrow bandwidth that it lends itself to projection of the frustration you feel as a frustration with your audience. That is, I believe, a hazard of the medium, which should be the real object of this frustration. To communicate this way requires a tremendous self-discipline. You have the notion that you are being more patient than a saint in expressing yourself, yet in fact it is simply a consequence of the medium that you have to do that. You are not really being patient with your audience, as you tend to feel, but being patient with this extremely limited way of expressing things.Brews ohare (talk) 16:17, 16 July 2008 (UTC)

Part 4

This does not mean I disagree with you. Just that I find it hard to convince others that the imaginary force "experienced" by the car driver driving along an S-shaped trajectory is not centrifugal, in the driver's own natural frame of reference (i.e. his own LCS). This terminology does not seem to be based on math (math is neutral in this respect, in my opinion; you and Brews are both right about math); it seems to be also based on a philosophy and terminology which is meant to be intuitively appealing for laymen who don't have a good grasp of physics. Paolo.dL (talk) 23:31, 15 July 2008 (UTC)

I cannot follow these remarks. In the driver's LCS (as you call it) there is no centripetal force because the driver is at rest. To reconcile his observed need for a force to maintain his S-shaped path, he must combat a centrifugal force. A possible way to look at things is simply to imagine the S-shaped path to actually be two half-circles of fixed radius. Then you can see at once that the analysis for nonuniform circular motion applies, and the general analysis agrees exactly with that more restricted analysis in that case. Brews ohare (talk) 12:59, 16 July 2008 (UTC)

No centripetal force? The driver must "combat a centrifugal force"? Nonsense. And we don't need your simplification to understand the concept of instantaneous centripetal acceleration in a curvilinear and non-circular path. Paolo.dL (talk) 14:19, 16 July 2008 (UTC)

Why is it nonsense to use two half-circles as a simplified example? Any discussion of the S-curve has to agree with this case as a limiting case. Brews ohare (talk) 14:23, 16 July 2008 (UTC)

Please read before answering! You keep missing my point. Paolo.dL (talk) 14:31, 16 July 2008 (UTC)

Here is my view. Please take the time to tell me where I miss your point.

If I use the two-half circle simple case, then while the particle is on the lower half circle the analysis in the inertial frame can be based upon either a coordinate system centered at the axis of rotation, or it can be based upon an arc length description. Both approaches lead to exactly the same centripetal and tangential accelerations. See this circular motion example in article Centripetal force. Switching to the particle's non-inertial frame where it is at rest, its centrifugal force is exactly the opposite to the inertial observer's centripetal force. The particle's Euler force is exactly opposite to the inertial observer's tangential force. Thus, in the lower circle of the S-curve, the general analysis agrees exactly with this analysis based on nonuniform circular motion. The argument can then be repeated for the upper half-circle of the S-curve. However, the coordinate system of the inertial observer now can retain the same arc length coordinate system as for the lower half, or equally, may adopt a circular coordinate system with the new center of rotation. I believe that examination of this simplified case leads readily to the general case. Brews ohare (talk) 03:01, 17 July 2008 (UTC)

Non-fixed axis

Figure 1: Precession of the frame of a gyroscope. The second and third Euler angles of the frame are constant

Note: This section is about this figure recently added by Brews to the introduction, and removed by Paolo. Paolo.dL (talk) 18:12, 16 July 2008 (UTC)

The figure added and then removed by Paolo simply illustrates a case where the direction of an axis about which rotation is occurring is itself changing direction. This animation is a very nice illustration of a case where the analysis of the article does not apply, and is meant simply to provide a concrete illustration that there is a lot more to the problem than this article can deal with. For the general reader it is a very visual example and should be retained. In any event, the possibility of its removal is worthy of discussion here. Brews ohare (talk) 12:13, 16 July 2008 (UTC)

I don't think the figure is really an appropriate choice for the first figure in the article. I would think that should be an image which illustrates centrifugal force as simply as possible. In any case, if the figure stays, it needs more explaining. It is currently not made clear that the wheel of the gyroscope is spinning as well as precessing, and that the frame being referred to is fixed to the wheel. One other consideration is that the figure is on the large side, which may be of concern to users with slow internet connections. Rracecarr (talk) 12:47, 16 July 2008 (UTC)

Good points. Maybe the article should be rearranged to put the examples earlier; and all the caveats and confusion later? In the meantime, I've improved the discussion of this figure. Brews ohare (talk) 13:05, 16 July 2008 (UTC)

I removed the figure and explained my rationale on Brews's talk page:

A precession can be (and typically is) a rotation about a rotating axis. But the picture you added showed a rotation about a fixed vertical axis (i.e. a precession with same angular velocity as the rotation about the "south-north" axis of the object). Besides that, the example about precession is too difficult to understand for an introduction about centrifugal force (because people thinks that the instantaneous axis of rotation is the "south-north" axis, which is never true). A much better example about rotation about a non-fixed axis was about the "particle along S-shaped trajectory".

However, I fail to understand the reason why you want to talk about rigid bodies and Newton-Euler equations in the introduction. I suggest to open a new section at the end of the article about this topic. But it would just say that:

1. either you study the motion of the body CM, and in this case centrifugal force is computed as if the body were a point mass, or
2. you study the motion of a particle in the rigid body which does not coincide with the CM; then you just compute the kinematics of that particle, then you again use the formula for particles.

I mean, the same formulas for centrifugal force as those you use for particles can be applied to rigid bodies. IMO, this is not something worth mention in the introduction. By the way, I guess you agree that inertial couples (appearing together with fictitious forces in adjusted Newton-Euler equations used within non-inertial frames) definitely do not belong in this article! Paolo.dL (talk) 09:38, 16 July 2008 (UTC)

Brews, would you mind to explain why you ignored my message on your talk page and reinserted the figure before discussing my rationale? Paolo.dL (talk) 13:20, 16 July 2008 (UTC)

Paolo: I've followed your suggestion and removed the image from the Introduction to a new section; an improved description is provided. BTW, can you explain why you deleted the image without any talk-page discussion? Brews ohare (talk) 13:55, 16 July 2008 (UTC)

Thank you. I posted a long explanation on your talk page, even before you opened this section here. Have you read it? Also, you recently removed an entire paragraph without first discussing it. This should not be a problem, unless you refuse to discuss your deletion or changes. But if you want to propose a different policy, just ask and I will follow it, provided we all agree to do the same (you included). Paolo.dL (talk) 14:28, 16 July 2008 (UTC)

Brews, you force me to yet another repetition: have you read my explanation on your talk page, that I copied above after you ignored it? Do you realize that by moving the figure to another part of the article, after reinserting it, you are still ignoring the explanation I gave you when I removed it from the article? The whole "frame" of the gyroscope (see figure caption) clearly rotates about a fixed vertical axis. Don't you think you should take a decision about a discussed topic, and edit, only after understanding the relevant discussion? Paolo.dL (talk) 18:28, 16 July 2008 (UTC)

Some confusion here: I see more than one rotation involved here: the gyroscope rotates about its own axis and then besides that the axis of the gyroscope rotates about a fixed vertical axis. It is both of these movements that make the problem more complex. Don't you agree? I introduced this figure because it became clear to me that most contributors to the various articles treat only rotation about a fixed axis, in my opinion because that example is all they thought about. I thought it useful to have a figure that showed things could be more interesting than that, without intending to go into any detail about it. Brews ohare (talk) 22:54, 16 July 2008 (UTC)

Yes, some confusion. You don't even understand the caption of the figure, do you? Of course, it doesn't matter if you don't understand. I will be glad to explain. Actually, nobody's knowledge is flawless, and when I did not understand that a centrifugal force existed even when the net fictitious force was centripetal, you were the one who patiently explained it to me.

The main problem is another: you have ignored my edit summary and my repeated explanations. You totally ignored them, and just reinserted your picture. This is an intolerable behaviour, in my opinion, because it is an interaction denial. Without interaction, the only alternatives are an edit war or a painful arbitration. You are a precious editor, your pictures are great, your edits are massive and brilliant (although honestly not always well readable, and sometimes questionable). Why can't you just follow the rules that permit collaboration between editors? Would you mind to remove the picture and wait for the end of this discussion before taking a final decision about this paragraph? Thank you. Paolo.dL (talk) 21:04, 17 July 2008 (UTC)

Hi Paolo: I don't see a pressing need to remove this figure before the discussion is resolved. It is not misleading any reader, as things stand.

Let me see if I understand your points:

1 I fail to understand the reason why you want to talk about rigid bodies and Newton-Euler equations.

Maybe that point is clear now: the aim was simply to show a more general situation.

2 The whole "frame" of the gyroscope (see figure caption) clearly rotates about a fixed vertical axis.

I haven't understood what this has to do with anything. First, the axis of rotation is changing direction by rotating around the z-axis. Isn't that enough of a different case to make the reader understand that rotation about a fixed axis is a simple-minded case?

3 I mean, the same formulas for centrifugal force as those you use for particles can be applied to rigid bodies. IMO, this is not something worth mention in the introduction.

It is the idea of changing direction of the axis that bothers me. I don't think the formulas for rotation about a fixed axis are readily applied when the axis is changing orientation. Am I wrong about that? Maybe you have an example? Brews ohare (talk) 21:50, 17 July 2008 (UTC)

Questions for Paolo.dL

Paolo.dL, I have been watching this discussion page and I have got a few questions to ask you. I was blocked from editing for a month and so I wasn't able to come in to the discussion when you entered it towards the end of June.

When you first entered the discussion, my understanding was that you were advocating about three key points. However, as the discussion progressed, I lost touch with what points you were trying to make.

Am I correct in believing that you were trying to say that "actual" tangential motion of an object relative to a point origin is necessary in order to obtain centrifugal force? That is certainly the point that I was trying to make. I have been trying to tell them all that centrifugal force is not a topic which is exclusively tied up with rotating frames of reference, and that when it is so tied up, the centrifugal force term in the transformation equations only applies to objects that are constrained to co-rotate with the rotating reference frame.

These guys here seem to think that centrifugal force acts on objects that are stationary relative to a rotating frame of reference. Their belief was long ago disproved by Newton's Bucket argument yet they cite an article in a 1967 physics journal as being the definitive word on the matter.

Unfortunately, the high quality textbooks are silent on the matter. For example, Goldstein's 'Classical Mechanics' introduces the topic of rotating frames of reference. It then derives transformation equations in which the centrifugal and Coriolis terms would apply to co-rotating objects. However, Goldstein, despite the fact that all the worked examples involve co-rotation, fails to explicitly state that the equations only apply to co-rotation.

I have tried to carefully explain to these guys how the derivation makes co-rotation a prerequisite for the applicability of the equations, but my explanations are consistently ignored. They demand citations, and when I gave them one citation from a GD Scott article, they point blank refused to accept that GD Scott meant what he said.

Another important point is that these guys refuse to look at more general curved path motions. They restrict their discussion exclusively to circular motion examples in which the associated equalities mask the important details. Try introducing an elliptical motion example and they will delete it instantly. David Tombe (talk) 22:01, 17 July 2008 (UTC)

Hi David. I am sorry you were blocked for a month. I think that was excessive. I think you have a right to express your opinions here, even if they're wrong.

I don't think you will find Paolo to be a useful ally in getting the stuff you want in the article. He clashes with other editors, in some cases the same ones you do, but he understands the basic idea, which you do not (you think you do, I know, but you are wrong). Incidentally, that is another difference between you and Paolo: he sometimes is convinced by argument. He has argued with other editors and sometimes come to see things their way. You never admit for one second the possibility that you might not be entirely correct. You should try to change that attitude. Rracecarr (talk) 22:03, 18 July 2008 (UTC)

Rracecarr, I noticed while blocked that Paolo.dL had come into conflict with the majority of the editors here, and so I am now trying to get a clearer picture of what the key points of his argument are.

Meanwhile, I ought to re-iterate to you what my own main argument is. Both centrifugal force and Coriolis force are perpendicular deflections. A rotating frame of reference superimposes a circular motion on top of the already existing motion. This superimposition should not be confused with centrifugal force and/or Coriolis force.

Rotating frames of reference are a topic in applied maths that involves both centrifugal force and Coriolis force. However, centrifugal force as a topic in its own right does not need to be discussed in connection with rotating frames of reference.

Finally, the rotating frame of reference transformation equations only actually apply to objects that are physically constrained to co-rotating radial motion within the rotating frame.

You have been applying these equations wrongly in order to explain the superimposed circular motion in terms of both centrifugal force and Coriolis force. David Tombe (talk) 12:57, 19 July 2008 (UTC)

Write on the blackboard 100 times:

In an inertial frame there is no centrifugal force. In a rotating frame the centrifugal force does not depend on the motion of the object.

In an inertial frame there is no centrifugal force. In a rotating frame the centrifugal force does not depend on the motion of the object.

In an inertial frame there is no centrifugal force. In a rotating frame the centrifugal force does not depend...

Rracecarr (talk) 13:26, 19 July 2008 (UTC)

Rracecarr: You are beginning to lose your "cool" here, eh? Brews ohare (talk) 14:15, 19 July 2008 (UTC)

Actually, I don't think I'm losing my cool at all, if I ever had any. DT is completely impervious to rational argument, so why not try humor? Rracecarr (talk) 15:46, 19 July 2008 (UTC)

RRacecarr, centrifugal force is a radial force that can be described using polar coordinates in an inertial frame of reference.

In a rotating frame of reference, a circular motion is superimposed on top of all existing motion. If the object is stationary in the inertial frame, there will be no centrifugal force acting on it. The circular path that it appears to trace out as viewed from the rotating frame does not imply the existence of any centrifugal force. There is clearly no radial acceleration involved.

Your big mistake is in believing that this artificial circle can be constructed mathematically from a centrifugal force and a Coriolis force. It can't. I've already explained why on many occasions.

The equations that you are using to support your ideas have derivations which involve restrictions that you are deliberately ignoring. In fact, the rotating frame transformation equations are derived in exactly the same manner as are the expressions for acceleration in polar coordinates, and they lead to exactly those same expressions. From that alone, you should be able to see that Coriolis force is a purely tangential effect.

You cannot swing Coriolis force around into the radial direction and pretend that it is overriding an equally bogus centrifugal force.

The derivation involves an angular speed. That angular speed appears in the centrifugal force term and it is the angular speed of the particle under consideration. Hence the centrifugal force term only applies to particles that possess that angular speed, ie. co-rotating particles. It does not apply to particles that are sitting stationary in the inertial frame.

So you are quite wrong when you say that centrifugal force is independent of the motion of a particle in a rotating frame. The tangential motion of a particle in a rotating frame increases or slackens the radial centrifugal force.

East/West motion of air into a cyclone increases or decreases the already existing centrifugal force. But unfortunately, you have been trained to believe that these deflections of east/west motion are Coriolis force. David Tombe (talk) 17:19, 19 July 2008 (UTC)

Only circular motion examples

Hi David. It's no longer true that we have only circular motion. See general planar motion. However, it is still true that I believe co-rotation is not mandatory for fictitious forces.

I'm sure long polemics can result from that remark. However, let me open by asking how you would handle the "rotating spheres" general case example. There, depending upon whether the rotating frame moves faster or slower than the actual rate of rotating of the spheres, the fictitious force can be centrifugal or centripetal. The fictitious force is mandatory to obtain the observed upon tension in the string, which is identical for all observers, inertial or otherwise.

Here is the question: how will you obtain agreement upon the measured tension if the fictitious forces go away when the spheres are at rest but the frame rotates?

How about when the frame rotates faster than the spheres, but both rotate?

How about when the frame rotates slower than the spheres, but both rotate? Brews ohare (talk) 22:55, 17 July 2008 (UTC)

Brews, in reply to your questions, the rotating frame of reference has got absolutely no physical significance whatsoever. It has no effect on the motion. The centrifugal force is a radially outward effect which will be determined exclusively by the tangential speed of an object relative to a point origin.

Hence in a co-rotating marble, such as is constrained to move in a radial groove in a rotating turntable, the marble itself will possess the same angular speed as the rotating frame and so there will be no ambiguity.

However, in a case of partial co-rotation, the only factor that will be relevant will be the actual angular speed of the object that is experiencing the centrifugal force.

This article could be drastically simplified, perhaps even to one line. At the moment, the article is far too incoherent and it contains far too many irrelevancies. For example, there is no need to introduce gyroscopes to this article at all.

The article could be replaced by a single sentence which would read as follows,

"When an object moves, it will have an outward radial acceleration relative to any point origin, that is determined exclusively by its tangential speed relative to that point".

We need to generalize the scenarios even beyond curved path motion. We don't exclusively need curved path motion. Even straight line motion contains a centrifugal force relative to points that are not on its path. David Tombe (talk) 17:35, 18 July 2008 (UTC)

One-sentence article

"When an object moves, it will have an outward radial acceleration relative to any point origin, that is determined exclusively by its tangential speed relative to that point".

Hi David: Well, one-sentence summaries are a risky business. This one doesn't seem to fit in with your preconceptions very well. For example, what if the "point origin" is made to move? Does that increase the radial outward acceleration of the object? And how do I know if the object is moving, or if its movement is only apparent, due to movement of the point origin? Brews ohare (talk) 18:49, 18 July 2008 (UTC)

Brews, it doesn't matter whether the point origin is in motion or not, and the question of how we would actually determine whether or not the point origin is in motion or not is secondary to this issue. Centrifugal force is a mathematical reality irrespective of its actual physical cause. Its physical cause has never been debated on these pages and there is no existing official consensus on the matter.

I will soon be writing an article on the cause of centrifugal force but it will be original research and it will not be discussed on these pages.

The only undisputable fact is that an object that moves relative to a point in space (the point being either moving or stationary) will experience an outward acceleration relative to that point given by the expression rω^2 where ω is the angular speed that derives from the tangential speed relative to that point, and r is the radial distance between the point and the object.

We could make this whole article a one sentence article and bring it into line with standard encyclopaediae. David Tombe (talk) 19:40, 18 July 2008 (UTC)

Brews, it doesn't matter whether the point origin is in motion or not, and the question of how we would actually determine whether or not the point origin is in motion or not is secondary to this issue.

David: Your remarks indicate centrifugal force relates only to relative motion of the object and the point of origin. I thought your position was different. I thought your position was that centrifugal force depends on the "real" motion of the object, and that there is zero centrifugal force upon an object that "really" is not moving but only appears to move because the frame is moving. That is, in your opinion, if the object does not co-rotate, but only the frame rotates, there is no centrifugal force. Brews ohare (talk) 21:59, 18 July 2008 (UTC)

Brews, in order to obtain centrifugal force, we need to have "actual" tangential motion relative to a point origin. The question then arises as to what do we mean by "actual" tangential motion. The answer is that "actual" tangential motion is tangential motion that is referenced to the background stars.

That of course opens up more questions. But meanwhile we are left with the reality that centrifugal force is a real outward radial force that occurs on all objects that move tangentially relative to a point origin.

I will soon have an article that discusses the possible physical cause of centrifugal force. You will find it if you want to, but it won't be on these pages as it will be original research.

Getting back to the artificial circle again, there is absolutely no centrifugal force involved as there is no tangential motion involved, relative to the background stars. Your attempts to justify the superimposed circular motion mathematically in terms of centrifugal force and Coriolis force are wrong on many counts.David Tombe (talk) 13:09, 19 July 2008 (UTC)

Hi David: I gather that the "one-sentence" summary is not really a "stand-alone", but is to be supported by a forthcoming article. However, while awaiting that event, we now might revise the one sentence summary as follows:

"When an object moves relative to the fixed stars, it will have an outward radial acceleration relative to any point origin, that is determined exclusively by its tangential speed relative to that point".

If that is a more accurate statement, it still suggests that the motion of the point origin relative to the fixed stars affects the centrifugal force, in your opinion. Is that an accurate reflection of your opinion? Brews ohare (talk) 14:01, 19 July 2008 (UTC)

Brews, Mutual tangential motion relative to the background stars is the accurate way to describe it. So in that case, yes I stand corrected and now accept that the motion of the origin is also relevant when we are talking about mutual tangential motion.

But in your artificial circle scenario, there is no mutual tangential motion. That has been my point all along. Without that actual tangential motion, there will be no induced outward radial acceleration. There will be no centrifugal force.

You and RRacecarr are trying to justify the artificial circle mathematically in terms of both centrifugal force and an inward radial Coriolis force. What you are doing is quite wrong. The artificial circle is a superimposition. It cannot be justified in terms of a summation of centrifugal and Coriolis force. The centrifugal force and the Coriolis force are perpendicular deflections. They are not superimpositions.

When there is no mutual tangential speed, there will be no centrifugal force.

You have been clouding up all the examples of centrifugal force by adding in the extra and unnecessary complications of considering these examples from rotating frames of reference. There is no need to do that. There will either be centrifugal force or there won't. It doesn't matter what reference frame we observe it from.David Tombe (talk) 16:57, 19 July 2008 (UTC)

Hi David: I'm proceeding only one step at a time, because I want to be completely clear what the one-sentence summary means. Above you have said:

Brews, Mutual tangential motion relative to the background stars is the accurate way to describe it. So in that case, yes I stand corrected and now accept that the motion of the origin is also relevant when we are talking about mutual tangential motion.

Proceeding from that point, it seems that the origin point may move relative to the fixed stars and the object can be stationary, and as their relative motion is not zero wrt to the fixed stars (and wrt to each other, it might be added) a centrifugal force will exist. Am I on track? Brews ohare (talk) 17:44, 19 July 2008 (UTC)

Brews, Yes. Providing that we are talking exclusively about tangential motion. It is tangential motion that induces radial centrifugal force. As somebody interested in electromagnetic induction, I thought that you might have seen the connection already.

Why did you switch your interest so suddenly from electromagnetism to centrifugal force? On my part, I have been interested in the connection since I read Maxwell's 1861 paper in 2005.

It's EM induction that got me interested in centrifugal force via Maxwell's sea of molecular vortices. I notice that you were recently very interested in the meaning of the A vector and the vXB force.

Then you jumped to centrifugal force. Well you came to the right place, but I have seen no evidence yet that you have seen the connection.David Tombe (talk) 22:08, 19 July 2008 (UTC)

Observer in frame S circling a stationary object in frame S' . Left panel: Inertial frame fixed wrt fixed stars; Right panel: Motion of stationary object as seen by the observer in S. Radius vectors from the origin of moving frame S to the object at times t₀, t₁, t₂ are R₀, R₁, R₂

Hi David: I see that I need to be able to recognize tangential motion. For example, if the object is stationary wrt the fixed stars and the origin point is translating at uniform velocity v in the x-direction, also wrt to the fixed stars, is that relative tangential motion? Or, as a different case, if the origin point is circling the object at an (instantaneous) radius R and at this same instant is moving at velocity v in the x-direction is that tangential motion? I suspect that although they may both exhibit tangential motion, only the case with finite curvature leads to any force due to tangential motion.

Assuming that to be the case, which object is subject to the force arising from tangential motion? The moving observer at the origin point or the stationary object? And according to whom? I made a figure of the simple case of circular motion to help discussion. At time t₀ the moving observer is at the bottom of the circle with instantaneous velocity v = υ i. At times t₁, t₂ the observer has moved further around the circle. The stationary object appears to circle the observer (right panel).

If we are the observer at the moving origin point, by definition of this observer, he believes himself at rest. Yet he sees the object circling him, while subject to no attracting body or other recognized source of influence. Therefore, he must posit a force that has no known physical source to provide the centripetal force that his kinematics demands for any object in circular motion. (For example, there is no evidence of a gravitational body, an electric charge, and so forth; nothing to put into Newton's second law as predicted by the Standard Model or whatever model.)

All this applies equally to any path for the moving origin point that has curvature, not just circular motion. Because any path with curvature leads via kinematics to a force requirement that can be met only by positing a fictitious force. How am I doing so far? Brews ohare (talk) 22:40, 19 July 2008 (UTC)

Brews, I fully accept that there are cases of centrifugal force which are nothing more than a mathematical artifact without any associated physical cause or physical reality. Examples of this would be the radial expansion of a line drawn between a particle moving in a straight line and a purely imaginary point origin. There are also cases of centrifugal force that would appear to have a physical cause and a physical reality. Planetary orbital theory is the prime example of the latter.

It is important that we draw a distinction between these two kinds of centrifugal force.

As regards the kind that probably does involve a physical cause, ie. planetary orbits, we are effectively in the same boat as is the case with gravity. We can do it all mathematically without consideration of any physical cause. Even Newton, who suspected aether inflow theory to be the cause of gravity, was never confident enough to make an issue of this belief. He concentrated exclusively on the mathematical description of the effect.

It gets more interesting however when we move over to magnetism. Maxwell extrapolates centrifugal force to the extent that a very real centrifugal force will repel two vortices that are aligned in their equatorial plane. According to Maxwell, this is the centrifugal force that we feel when we try to push two like magnetic poles together. That is no artifact.

That is the subject that I am currently investigating.

On the main article, there exists one very interesting section entitled 'Potential Energy'. I'm surprised that this section has survived Anome's purges. That section is perhaps the most useful section on the entire page in terms of pointing us in the direction of the underlying cause behind centrifugal force.

Now to answer your specific questions, you will have to get into the way of thinking in terms of the radial and the tangential direction. These are the only two directions that have any physical significance on the microscopic or the cosmological scale. Cartesian X, Y, Z is a language which is quite simply not suitable for the purposes of analyzing centrifugal force.

You should understand the concept of the tangential direction as a matter of course. I shouldn't have to explain it to you. If the Moon had no tangential motion relative to the background stars, it would fall to Earth radially.

Your examples about the imaginary point origin moving are examples of centrifugal force that are only mathematical artifacts.

But your artificial circle example is not even a mathematical artifact. It is nothing. It involves no centrifugal force in any shape or form, either mathematical or physical. There is no radial acceleration involved. A rotating frame of reference cannot even create a radial artifact, never mind a real centrifugal force. David Tombe (talk) 12:38, 20 July 2008 (UTC)

Sorry David, I don't find an answer above to these questions:

Hi David: I see that I need to be able to recognize tangential motion. For example, if the object is stationary wrt the fixed stars and the origin point is translating at uniform velocity v in the x-direction, also wrt to the fixed stars, is that relative tangential motion? Or, as a different case, if the origin point is circling the object at an (instantaneous) radius R and at this same instant is moving at velocity v in the x-direction is that tangential motion?

To these questions I'd like to add: Does tangential motion (which I hope you will define) always lead to "real" centrifugal force? Or, does it sometimes lead to "mathematical artifact" centrifugal force? Brews ohare (talk) 13:55, 20 July 2008 (UTC)

Brews, it sometimes leads to 'mathematical artifact' centrifugal force. The best example of mathematical artifact centrifugal force is two imaginary points moving in straight lines and possessing mutual tangential speed. There will be an induced outward radial centrifugal force acting between them. It will be mathematically real but it will possess no physical significance.

Regarding the meaning of tangential, I don't know why you insist on having to have this explained to you in terms of an x-direction. Can you not simply understand the concept in its own right?

Radial motion relates to the distance between two points. Tangential motion is perpendicular to radial motion and it induces a radial acceleration.

I'm not quite sure if you are being genuine as regards your enquiry about the meaning of tangential. It is a trivial issue which most people take for granted. You should try not to filibuster the more important issues by getting the discussion sidetracked into pedantic trivia such as discussing the meaning of 'tangential'. In doing so you are ignoring all the interesting questions such as the link between electromagnetism and centrifugal force. David Tombe (talk) 14:41, 20 July 2008 (UTC)

Hi David: I'm just trying to be sure that we use terminology the same way, as I have found that to be a major stumbling block in this type of interchange. To that end, am I to understand that any two points in relative motion exhibit tangential motion? For example, a stationary object and a moving origin point that is moving without acceleration of any kind, exhibit tangential motion? In that case, kinematically speaking, straight-line motion requires no force, applying Newton's first law, so tangential motion would not generate centrifugal force in this case. Brews ohare (talk) 15:23, 20 July 2008 (UTC)

Brews, Tangential motion is perpendicular to radial motion. It only has any meaning when it is referenced to the background stars, because in that case it results in outward radial acceleration.

Just imagine two points passing each other but not colliding. The tangential motion is the component of the motion of each particle that is perpendicular to the line that connects the two points. The radial motion is the motion that affects the distance between the two points.

All tangential speed will be accompanied by an outward radial acceleration given by v^2/r, where v is the tangential speed and r is the distance between the two points.

That is centrifugal force in a nutshell. But it doesn't tell us very much about the underlying physics or the nature of any associated potential energy.

The underlying physics has not yet appeared in the textbooks, just as the underlying physics behind the force of gravity has not yet appeared in the textbooks. David Tombe (talk) 18:40, 20 July 2008 (UTC)

Hi David: So the long and the short of it is that two bodies, both moving in straight-line motion relative to the fixed stars, but in paths that are skew (i.e. are neither parallel nor intersecting) will exhibit both tangential motion and also centrifugal force. Is that your statement? Assuming the answer is "yes", do both bodies experience this force, and is it equal and opposite for each? Brews ohare (talk) 22:23, 20 July 2008 (UTC)

The underlying physics has not yet appeared in the textbooks, just as the underlying physics behind the force of gravity has not yet appeared in the textbooks. David Tombe (talk) 18:40, 20 July 2008 (UTC)

O rly? And all this time I was thinking the theory of general relativity described the underlying physics of gravity. (At least at the macroscopic scale where the concepts of space and time (and spacetime) make sense.) Really, David I suggest you try learning GR. It will also clear up many of your misconceptions about centrifugal forces. And instead focusing on the ramblings of Maxwell from the 19th century, I suggest you have a look at the covariant formalism for electromagnetism. It sheds a lot of light on many of the things the 19th century phycists were confused about. (TimothyRias (talk) 13:22, 28 July 2008 (UTC))

Timothy, we'll have to agree to differ there. You talk about the ramblings of Maxwell. You are overlooking the fact that he led us to the standard equations of electromagnetism that we use today. You may argue that we can obtain these same equations using relativity. Well I disagree. Maxwell and relativity don't mix. The reason why I have sided with Maxwell is because we need to have a physical explanation for the displacement current. The textbook derivation of Maxwell's displacement current is flawed. I'm sure that you would agree with the textbook derivation but there's nothing I can do about that. Don't assume that I am not familiar with relativity. The difference between you and I is that I scrutinize these things to make sure that there are no flaws in the derivations. And that gets us back to centrifugal force. You come back after a few months as if all those arguments we had about rotating frames never happened. I showed you exactly where the flaws were in your extrapolation of those equations to particles that are stationary in the inertial frame. You used every trick in the book to wriggle out of having to acknowledge those flaws. You tried to cloud the whole issue up by introducing the three body problem. You tried to cloud it up by allowing the reference point in the rotating frame to be in motion relative to the rotating frame. And now you are pulling the oldest trick in the book. You are returning as if those arguments never took place and that your own understanding of centrifugal force is perfect. David Tombe (talk) 19:09, 28 July 2008 (UTC)

Don't insult my intelligence. The only thing you managed to do in the previous discussion is demonstrate how little you actually know and understand about both mathematics and physics. At some point I just realized there was very little point in trying to educate you an decided to stop wasting my time and energy. Your remark above about Maxwell and relativity not mixing is a prime example of your ignorance. It is the Maxwell equations that lead to special relativity. Maxwell was to stuck in the paradigm of absolute time to realize this, and it took the brilliance of Lorentz and Einstein to see the true depth of the Maxwell equations. The physical explanation of the displacement current is simply that nature possesses a U(1) gauge symmetry, that symmetry completely fixes the Maxwell equations.

And from your writings its pretty easy to deduce that you are completely unfamiliar with the contents of general relativity. Otherwise you would for one know that it in fact identifies gravity as just another inertial force, which results from using coordinates in which geodesics are not straight lines. You would also not be making silly mistakes resulting from erroneously identifying the tangent spaces of different points. So it seems very safe to assume that you have very little knowledge of general relativity. That is the true difference between you and me. I have actually understood the underlying physics, while you seem to be milling in the same confusion that the 19th century physicists were struggling with. (TimothyRias (talk) 22:15, 28 July 2008 (UTC))

Timothy, I'm not going to get dragged into an argument about relativity. If you want to believe in relativity, that's your business. I don't argue about relativity. David Tombe (talk) 00:16, 29 July 2008 (UTC)

Scope of the article

[NOTE: The discussion about this topic started in a previous section. Paolo.dL (talk) 11:24, 19 July 2008 (UTC)]

Paolo has removed the following material without discussion (from which I have dropped the original figure and here's another possibility):

Behavior of a reference frame embedded in a body, under modification of its Euler angles. Using x-y-z convention.

Scope of article

The table of contents suggests the content of this article, which is not an exhaustive treatment of the subject. Some very common situations are not included, one being the precession of the axis of a simple gyroscope: the gyroscope rotates about its own axis, while in turn its own axis can be made to rotate about a vertical fixed axis. Such compound motions lead to rather complicated fictitious forces, and are not treated here. The translation and rotation of a rigid body is governed by the Newton-Euler equations.

I see no harm in alerting the reader to more general cases and proving links where more information can be found. It is clear that the case of a fixed axis of rotation provides a good starting point, but it is easy to get the idea that it is the only case of importance. Anybody have suggestions? Brews ohare (talk) 22:19, 18 July 2008 (UTC)

I did not remove the section without discussion. I provided several times detailed explanations (see above). I removed it, I repeatedly explained why, Brews ignored my explanations and reinserted it, thus I was forced to remove it again. The main problem was the figure and its caption, as you can deduce from my last edit summary, on which I repeat a simple concept and explicitly refer to the relevant previous discussion:

/* Scope of the article */ See talk page. This section must be rewritten. Figure shows a motion about a SINGLE FIXED axis (as the caption explains) which is totally the opposite of what it should show [NOTE: this edit summary refers to the figure showing gyroscope precession]

The previous discussion was ignored by Brews, who confessed his "ignorance" explicitly in the first sentence of this section: "Paolo has removed the following material without discussion". Paolo.dL (talk) 10:39, 19 July 2008 (UTC)

Brews also ignored this comment:

The main problem is another: you have ignored my edit summary and my repeated explanations. You totally ignored them, and just reinserted your picture. This is an intolerable behaviour, in my opinion, because it is an interaction denial. Without interaction, the only alternatives are an edit war or a painful arbitration. You are a precious editor, your pictures are great, your edits are massive and brilliant (although honestly not always well readable, and sometimes questionable). Why can't you just follow the rules that permit collaboration between editors? Would you mind to remove the picture and wait for the end of this discussion before taking a final decision about this paragraph? Thank you. Paolo.dL (talk) 21:04, 17 July 2008 (UTC)

Following rules that permit collaboration between editors is extremely important. As soon as we set these rules and promise we'll respect them, I will be glad to discuss specific topics. By the way, Brews's new text (see above) contains a note written with sloppy language about which I repeatedly warned him and that I eventually fixed with a recent edit. This was my edit summary:

Brews, I warned you that the language in this reference was sloppy, and you reinserted it without even bothering to clean it up

Brews was able to ignore even this edit summary. I can't believe it:

1. I initially removed the note and in my edit summary I warned Brews that it contained sloppy language,
2. He ignored my explanation and reinserted it without changes (together with the above mentioned figure)
3. Rather than removing it again, I fixed it (I hate edit wars)
4. And here it is again, in Brews's new text (see above).

Yet another incredible example of Brews's "blindness" to the contribution of other editors. I need help by other editors. Brews is a precious editor, but his behaviour needs to be corrected. Paolo.dL (talk) 10:39, 19 July 2008 (UTC)

Well, I do not agree on this version of "history". Paolo already revised this section once, without discussion, and without objection from me. I provided several explanations that were ignored by Paolo. I have tried repeatedly to suggest that the original image involved two axes, not one. He insists that there is only one axis, which I cannot fathom: the gyroscope has an axis, and its axis precesses about a second axis. In any event, it is my view that the choice of image is a red herring. It also is my view that Paolo has not understood the purpose of this "scope" section, which is restated below, and ignored by Paolo. Brews ohare (talk) 14:08, 19 July 2008 (UTC)

Here is a quote from earlier discussion about the purpose of this section:

I see no harm in alerting the reader to more general cases and proving links where more information can be found. It is clear that the case of a fixed axis of rotation provides a good starting point, but it is easy to get the idea that it is the only case of importance. Anybody have suggestions? Brews ohare (talk) 14:10, 19 July 2008 (UTC)

As I pointed out several days ago, the source of confusion may be that it is not obvious from the gyro animation that the gyro wheel is spinning faster than the axis precesses. A second point that was never made explicitly clear in any version I saw is that the idea was to consider a frame of reference rotating with the wheel of the gyro, not just with the axis. Rracecarr (talk) 15:15, 19 July 2008 (UTC)

Your second point is accurate and helpful. The first point is neither here nor there. In any event the idea is to show a more complicated case than single fixed axis rotation. Editing the language to make this clearer would be helpful. Brews ohare (talk) 15:37, 19 July 2008 (UTC)

I disagree that the first point is not relevant. If the gyro wheel made one revolution per precession cycle, then Paolo would be right, and it would only be rotation about a single fixed axis. Rracecarr (talk) 15:40, 19 July 2008 (UTC)

Got it; thank you. Brews ohare (talk) 15:50, 19 July 2008 (UTC)

Thank you very much Rracecarr. I am glad that eventually Brews agreed. Not even my latest edit summary, nor the figure caption were enough for Brews. I was forced to fight an edit war to remove that picture, and had a very hard time trying to fight against Brews's repeated a priori rejection of my point. Here's the very first sentence of the explanation that I posted in Brews's user talk page and then I copied above, after Brews stubbornly reinserted his figure in the article:

A precession can be (and typically is) a rotation about a rotating axis. But the picture you added showed a rotation about a fixed vertical axis (i.e. a precession with same angular velocity as the rotation about the "south-north" axis of the object).

About the importance of a section about the scope of the article, I leave this discussion to others. It is a matter of opinion, and I am not used to impose opinions. More important points still need to be discussed. I just asked not to keep this paragraph in the introduction. Brews, can we work together more effectively in the future? Paolo.dL (talk) 21:03, 19 July 2008 (UTC)

Agreement n.2 reached

This section is about the figure showing gyroscope precession.

I am very happy to be able to write again a section with this title. I believe we all now agree on this (please correct me if I am wrong):

• The caption of the figure refers to a rotation of the frame of the gyroscope.
• The frame does not rotate about the axis of the gyroscope. It just rotates about a vertical fixed axis. A single axis.
• The caption confirms that the frame is rotating about a SINGLE FIXED axis, saying that only one of the Euler angles is changing.
• It is not obvious from the gyro animation that the gyro wheel is spinning faster than the axis precesses (the caption does not even refer to the rotation of the gyro wheel. It refers to the rotation of its frame).
• Thus, what the figure shows is totally the opposite of what it should show. Brews's sentence referred to the rotation of a gyroscope wheel, i.e a combined rotation, i.e. a precession, i.e. a rotation about a rotating axis, i.e a rotation which involves change in direction of the angular velocity vector. The figure, on the contrary, showed a rotation with constant vertical angular velocity.

Paolo.dL (talk) 21:03, 19 July 2008 (UTC)

About the new figure

Now, what about the new figure? Is there anybody who would like to help Brews to find a better figure? We need a figure showing a precession (for instance a twisting diver/gymnast, or the precession of a spinning top or just the previous figure modified to show the quick rotation of the gyroscope wheel, and with a different caption rewritten from scratch; any of these or something else, but whatever it is, it should be in slow motion, otherwise it would be impossible to understand). I guess the precession of our planet is not quick enough to be interesting in this context.

The new figure proposed by Brews (see above) is not good enough. It shows three successive (not simultaneous) rotations about fixed axes. Moreover, it refers to the concept of Euler Angles. I strongly suggest to leave this concept out of this article, if possible. Centrifugal force is already a difficult topic. Let's spare the readers additional doubts. Paolo.dL (talk) 21:03, 19 July 2008 (UTC)

Coordinate systems and frames

[NOTE: The discussion about this topic started in a previous section. Paolo.dL (talk) 21:40, 19 July 2008 (UTC)

Paolo has deleted a note (quoted below), without discussion on this "talk" page, concerning the independence of one's choices for coordinate system and observational frame of reference:

[Note: coordinate systems and frames of reference are independent. A frame of reference refers to the state of motion of the observer. A coordinate system refers to a choice of language used to describe observations. Any frame of reference can choose to employ any coordinate system (polar, elliptical, curvilinear, …) to describe observations in that system. A change in coordinate system does not mean a change in frame of reference, and vice versa.]

Paolo's description of the rationale for this deletion on the "history" tab is : Coord. systems (CS) are strictly associated to reference frames (RF). RF, in physics, allow measurement of kinematic quantities. Cannot exist without a CS.

This rationale does not address the content of the deleted statement, which does not deny possible association of a reference frame to a coordinate system, but merely the plurality of this choice. In addition, the rationale is incorrect in that a reference frame can use vectors, which choice allows description of observations that are independent of any coordinate system.

Paolo's terminology "strictly associated" brings to mind Paolo's earlier remarks on the talk page. On the talk page Paolo suggested coordinate systems and observational frames of reference were the same thing. I answered with the excerpt below from earlier discussion, which Paolo did not address:

Response by Brews_ohare: No, we do not agree. There are two separate issues:

1. What is our frame of reference? Are we at rest relative to the fixed stars or relative to the Moon, for example.
2. How do we wish to describe what we see? Is it simplest to use arc length, circular coordinates, or what ever. Should the coordinates relate to the path or relate to our origin?

My impression is that you would not care to imagine an observer on the Earth using a coordinate system centered on the Moon to describe a satellite orbiting the Moon. But that is feasible, and the Earth observer then will include effects due to the Moon orbiting the Earth that are omitted by a Moon observer using the same coordinate system to describe the satellite circling the Moon. Approximating the Earth as a frame more nearly an inertial frame than the Moon, the Moon observer will need to add fictitious forces. Brews ohare (talk) 14:59, 16 July 2008 (UTC)

Additionally, the example of an "arc-length" description of motion by both the moving and stationary observers is discussed at length in the article and in more detail in other articles as already pointed out to Paolo in earlier discussion.

The short version of all this discussion is: Choice of coordinate system and choice of frame of reference are distinct and separable, one's choice of one does not limit the choice of the other. That is what the deleted Note says, and it should remain in the article.

I believe it is reasonable that an active issue on the talk page be given some attention on this page before being deleted. Brews ohare (talk) 13:50, 19 July 2008 (UTC)

Please help - Wikipedia should be an orchestra

I am sick of these repeated lies. For the second time, Brews wrote above, at the beginning of a new section, the phrase: "without previous discussion". The discussion about this topic began in a previous section, and has not finished yet. Here's my recent edit summary:

Coord. systems (CS) are strictly associated to reference frames (RF). RF, in physics, allow measurement of kinematic quantities. Cannot exist without a CS

As I repeatedly pointed out previously, if two editors strongly disagree, the opinion of one of them cannot suddenly appear on the article, before an agreement is reached or at least the relative majority of the editors participating in the discussion agree! So, we should first discuss, hopefully with the help of others, then decide what we should write on the article.

Dear editors, can you see how many times I have to repeat this simple concept to Brews? Do you mind to help me to convince him? He likes to be a one-man-band. He is extremely talented, but Wikipedia is an orchestra. He perhaps deserves to be the prime violin, but should not be allowed to be a one-man-band. Please help me. Aren't there administrators in this group? Aren't there editors interested in symphonic music? Paolo.dL (talk) 22:02, 19 July 2008 (UTC)

Hi Paolo: I responded to this edit summary above. You have not provided any reply yet. Brews ohare (talk) 22:08, 19 July 2008 (UTC)

I know, and I will reply, of course. But, as I repeatedly pointed out, the main problem with you is another. You behave as the owner and treat others as guests. This makes cooperation too hard. The same happened when we discussed the gyroscope example (see previous section). Please remove again your controversial sentence about CS and RF, and wait for this discusion to end. Paolo.dL (talk) 22:15, 19 July 2008 (UTC)

Hi Paolo: Are we peers if this Note is arbitrarily removed until you eventually get around to discussing why it should be removed? My rather extended discussion is at Talk:Centrifugal_force#Coordinate_systems_and_frames. You have made no comment upon any of the points raised. Brews ohare (talk) 22:48, 19 July 2008 (UTC)

Brews, yes we are. I am convinced that your opinion about this topic is absolutely wrong, and the paragraph in the article expresses your own opinion. You need to admit that there are only two ways to be peer:

1. either we remove your controversial personal opinion from the article, and then we discuss or
2. I write another paragraph in the article explaining my opposite opinion, and then we discuss.

Now, would you mind to just guess what is the only one of these two possibilities which does not break Wikipedia policies? Another question: would you accept to keep my opinion on the article, if you were convinced it was wrong? Paolo.dL (talk) 21:00, 20 July 2008 (UTC)

Paolo: Yes, I do think you are wrong. I suggest you obtain some other opinions as mine doesn't carry weight with you. I'd recommend that be done before you present in the article what I believe to be an easily refutable erroneous opinion on this matter. Moreover, you will find nothing to cite on the matter in your support, and numerous counterexamples already have been pointed out to you. Moreover, you keep saying you will address these counterarguments, but you never do so. Brews ohare (talk) 22:17, 20 July 2008 (UTC)

And I do think you are wrong. So, at least in this respect we are peers. I do things one at a time. First, I want to convince you to work as a peer, not as the owner of this page. What is the only one of the above listed two possibilities which does not break Wikipedia policies? 1 or 2? Paolo.dL (talk) 22:29, 20 July 2008 (UTC)

I think you are avoiding the issue. I have no difficulty working with editors as a rule, and probably not with you either in general. But for this particular topic, I'd suggest you attempt to support your view and obtain some other editors' support. Brews ohare (talk) 22:34, 20 July 2008 (UTC)

The main issue under discussion here is that you want to impose your opinion. This is against Wikipedia policies. Your opinion will be expressed on the article if and only if we will agree or somebody else will "vote against me". Right now, your opinion has exactly the same weight as mine. If you agree on this rule, we will continue our discussion and you will possibly be able to prove you are right. I accept discussion only on a peer-to-peer basis. This is extremely important to me, and I hope that somebody else will help me to let you understand the importance of this principle. Paolo.dL (talk) 22:54, 20 July 2008 (UTC)

General advices

• I admit I haven't read this entire page as the subject is perhaps a bit over my head, but I think some of you that have been engaging in prolonged argument on this page might benefit from checking out some of the other 2,463,527 articles on Wikipedia, or maybe shutting off the computer and taking a walk or having a nice cup of tea. Sometimes the best way to resolve a debate is to let it go and come back later with a fresh attitude. You may even find you see things in a whole new light if you re-examine old issues. Beeblbrox (talk) 22:28, 19 July 2008 (UTC)

• After looking into all this a little more, I would also caution that Wikipedia is not the place for original research. If you are trying to prove something, either in the article or here on the talk page, you are in the wrong place. Only information which has already been published in reliable sources is acceptable content for a Wikipedia article. Beeblbrox (talk) 22:41, 19 July 2008 (UTC)

This talk page is becoming very long. Please consider archiving.

Gyroscopes should be on the Coriolis Force page

I don't know why gyroscopes are getting discussed on these pages. Gyroscope theory as per the textbooks involves neither centrifugal force nor Coriolis force.

My own personal opinion however is that the Coriolis force is heavily involved in gyroscope theory and that it is the reason why pivoted precessing gyroscopes don't topple over.

I have studied the official Lagrangian explanation in the textbooks in the greatest detail and I find it totally lacking as regards explaining why pivoted gyroscopes don't topple. There must be an extra force involved and it must take the form of vXω. This extra force is denied by modern physicists.

At any rate, all discussions about gyroscopes should be removed away from these pages and unto the Coriolis force pages.

We should be re-introducing the elliptical planetary orbit topic which is heavily related to centrifugal force.David Tombe (talk) 12:50, 20 July 2008 (UTC)

Centrifugal Potential Energy

It's true that Coriolis Force has no equivalent potential energy. It's also true that Coriolis force acts perpendicularly to the direction of motion and so it only acts to change the direction of a velocity and not the speed. Hence kinetic energy is conserved under the action of a Coriolis force.

However, centrifugal force also only acts perpendicularly to the direction of the motion.

Furthermore, any actual potential energy involved in examples of centrifugal potential energy are actually gravitational potential energy or hydrostatic pressure. We are witnessing centrifugal kinetic energy being converted into some other kind of potential energy.

In fact the so-called expression for centrifugal potential energy given in the article is in reality merely a kinetic energy term. The kinetic energy of rotation merely converts to potential energy of another kind. In that respect we can loosely refer to it as a centrifugal potential energy.

Centrifugal potential energy as such does not exist. Centrifugal force and Coriolis force stand in an identical situation in this regard as they are merely mutually perpendicular aspects of the same thing. David Tombe (talk) 14:56, 20 July 2008 (UTC)

Centrifugal force is not necessarily perpendicular to the motion, because it's formula involves only position, not velocity. In the rotating frame, where centrifugal force points radially outward and is always radial in direction, it is just like a fictitious radial gravity; thus, it can have a potential energy in the same sense that gravity does. This potential energy does not depend on the particular example given, where the Earth's gravity also is present. Brews ohare (talk) 15:15, 20 July 2008 (UTC)

OK Brews, let's go inside a rotating bucket of water. The water surface is curved up the sides of the bucket due to centrifugal force. Every element of water is co-rotating with the rotating frame. The centrifugal force is exactly perpendicular to the motion of every element of the water.

We're back once again to your denial of the fact that something needs to be co-rotating in order to experience centrifugal force.

So let's then consider a rotating bucket in which the water is not co-rotating. The water surface will be level. There will be no centrifugal force and no potential energy. In fact this is exactly the famous Bucket argument.

I can assure you that centrifugal force is always perpendicular to the motion that causes it just like Coriolis force and just like F = qvXB in electromagnetism.

Hi David: I didn't suggest that centrifugal force is never perpendicular to the motion, if that is your meaning. It is always radially outward from the axis of rotation, so it may or may not be perpendicular to any observed motion, depending on its direction. I do not believe the issue of co-rotation ever came up in my comments. Brews ohare (talk) 18:34, 20 July 2008 (UTC)

Brews, centrifugal force is always perpendicular to the component of the motion that causes it, just as Coriolis force is always perpendicular to the component of the motion that causes it. The former is the radial deflection of a tangential motion and the latter is the tangential deflection of a radial motion.

Regarding co-rotation, you brought the subject up indirectly when you suggested that centrifugal force is only position dependent in a rotating frame. It is also dependent on an angular velocity term. The dispute between us is that you think this angular velocity term applies to the rotating frame whereas I think that it applies to objects that are co-rotating in the rotating frame. In other words, centrifugal force is both position dependent and also dependent on the tangential speed of the object experiencing the centrifugal force. David Tombe (talk) 01:15, 21 July 2008 (UTC)

David: you have twice removed the phrase in italics from the sentence: "The Coriolis force has no equivalent potential, as it acts perpendicular to the velocity vector and hence rotates the direction of motion, but does not change the energy of a body." While this is not the only way of explaining why the Coriolis force has no associated potential while the centrifugal force does, it is a true statement (as you yourself have acknowledged), and you have not provided a good reason to remove it.Rracecarr (talk) 21:28, 20 July 2008 (UTC)

Rracecarr, the controversial expression contradicted the main part of the section, on the grounds that centrifugal force is also perpendicular to the direction of motion. Every element of water in the bucket that is experiencing centrifugal force radially outwards is moving perpendicularly to the direction of the centrifugal force. Based on the controversial sentence that you have restored, this means that there should be no such thing as centrifugal potential energy.

However, on further reflection, I have realized that I really should have deleted the main part of the section instead. There is no centrifugal potential energy. Look at the mathematical expression more closely. It is nothing more than the expression for the kinetic energy of an object in circular motion.

Lagrange must have a lot of potential energy, because he must certainly be spinning in his grave.- (User) WolfKeeper (Talk) 23:29, 22 July 2008 (UTC)

The same principles of energy conversion are applying in the rotating bucket of water as are applying in a planetary orbit. Kinetic energy converts to gravitational potential energy. Any potential energy in the rotating water is gravitational potential energy or hydrostatic pressure.

I should further add that if the water is not in a state of rotation, it will have no rotational kinetic energy to convert to gravitational potential energy. The so-called centrifugal potential energy that you are talking about only exists when the water is actually rotating. Yet you are trying to tell us all that centrifugal potential energy would exist if we viewed a stationary bucket of water from a rotating frame of reference. You must know fine well that observing a stationary bucket of water from a rotating frame will not make the water climb up the walls. There will be neither kinetic energy nor potential energy.

On the contrary, in the rotating frame of reference, each part of the stationary bucket has kinetic energy that exactly balances that of the centrifugal potential. In the rotating reference frame that stationary water has kinetic energy proportional to the square of the distance from the origin. It's exactly equal and opposite to the centrifugal potential energy, and because of that, the surface of the water has the same energy everywhere and no height gradient forms- you can take small bits of water and swap them, with no energy change, and hence no height change.- (User) WolfKeeper (Talk) 23:29, 22 July 2008 (UTC)

Are you going to try and tell me that the artificial circular motion that we would observe arises from a Coriolis force acting inwards (with no associated potential energy) and a centrifugal force acting outwards (with associated potential energy)? David Tombe (talk) 00:58, 21 July 2008 (UTC)

I am not going to try to tell you anything, because there's no point and it's not fun anymore. Please suggest potentially controversial changes here on the talk page before implementing them. Thanks. Rracecarr (talk) 03:48, 21 July 2008 (UTC)

I agree with Rracecarr. Moreover, this page is not meant to be a forum to defend personal opinions about the definition of the centrifugal force. I am sorry David Tombe, but this sentence of yours is wrong: "something needs to be co-rotating" [with the reference frame] "in order to experience centrifugal force" (and I suggest you not to use the word "experience" if you want to avoid subjective interpretations; use "be acted upon by"). We all agree, except for you, on the widely accepted definition of centrifugal force, which is already clearly explained in the article. Until you learn that definition, and study the numerous examples of its application provided in this article and in Fictitious force, you should not edit this article. And unless you accept to base your comments on that definition, you should not post in this page. Paolo.dL (talk) 22:09, 20 July 2008 (UTC)

Paolo.dl, If an object is stationary in the inertial frame, it will trace out a circle as viewed from the rotating frame. There will be absolutely no radial motion. So how can there be any centrifugal force? The expression for centrifugal force involves the tangential speed of the particle in question. If that tangential speed is zero, how can there be any centrifugal force?

So if an object is not co-rotating in a rotating frame, it will not experience any centrifugal force.

Just take a look at a stationary bucket of water from a rotating frame centred on the axis of the bucket. Does that make the water climb up the walls? No. So there is no centrifugal force and no centrifugal potential energy. David Tombe (talk) 01:07, 21 July 2008 (UTC)

Reply to RRacecarr on Coriolis Potential Energy

RRacecarr, you can't go storming in and reverting other peoples' edits and then come here stating that you are not willing to discuss the issue.

You have been advocating that centrifugal force and Coriolis force are both fictitious. Yet you are now claiming that while Coriolis force has got no associated potential energy, centrifugal force nevertheless has an associated potential energy which can cause rotating water to climb up the side walls of a bucket.

There are alot of matters connected with both centrifugal force and Coriolis force which you need to take a closer look at.

The section on centrifugal potential energy contains a contradiction which needs to be resolved. You know fine well that the water in the rotating bucket is moving perpendicularly to the centrifugal force. So you can't then go on and cite the fact that Coriolis force doesn't have a potential energy because it is perpendicular to the direction of motion.

Something in that section needs to be changed.

Either,

(1) the last sentence needs to be removed. Or,

(2) The last paragraph needs to be removed to the Coriolis force page and the rest of the section either deleted or entirely re-worded.

I would opt for the latter and re-word the remainder of the article to the extent that the term 'centrifugal potential energy' is really only a measure of rotational kinetic energy.

The stored energy in the rotating bucket is actually gravitational potential energy. It is not centrifugal potential energy. However it comes about as a result of the conversion of some rotational kinetic energy into gravitational potential energy as a result of centripetal force acting against the centrifugal force. So loosely we might say that the stored gravitational energy is centrifugal potential energy.

A similar situation can indeed occur with Coriolis force. A channel of water flowing along a radial drain pipe on a rotating turntable will have a similar gravitational potential energy as a result of the water being force up one side of the pipe tangentially.

And finally I should point out that according to your artificial circle theory which I totally disagree with, a Coriolis force acts radially inwards on stationary objects in the inertial frame, as viewed from a rotating frame. It has twice the magnitude of the centrifugal force and it takes on the same expression but with a factor of two, ie. 2mrω^2. Nonsense as this is, it is the core of the entire belief system of all the other active editors here. And on this basis, we can indeed construct a potential energy term from which to take a gradient and derive the Coriolis force.

So your entire belief system is totally confused and self contradictory.

If you are going to assume the role of unofficial guardian of the centrifugal force and Coriolis force pages, then you will need to learn to enter into constructive debate.

So far you have been relying entirely on your trump card which is that you have a large group of administrators who you can depend on to back you up in any edit war. David Tombe (talk) 10:24, 21 July 2008 (UTC)

There is no "constructive debate" with you--you don't listen. If you make bad edits, I will revert them. We can avoid that if you get consensus for your edits ahead of time.Rracecarr (talk) 13:37, 21 July 2008 (UTC)

No RRacecarr, You're the one that doesn't listen. I discuss things on the talk pages. I then make edits. You revert and then wrongly accuse me of not discussing it all first. Then when we go back to the talk pages you declare that you are not going to discuss anything.

This is because you operate in the full knowledge that you have a team of administrators behind you who will back you up everytime. This encyclopaedia operates on the principle of personality politics.

I have just noticed yet another flaw in the article. You state that Coriolis force is not position dependent. Yet your artificial circle theory depends on an expression for Coriolis force that is position dependent.

Your entire understanding of centrifugal force and Coriolis force has not been thought through properly. David Tombe (talk) 14:14, 21 July 2008 (UTC)

Hi David: You are getting a bit overheated and paranoid here. This venue for discussion lends itself to that, because it is a very slow process. Please take time to look at your frustrations as frustrations with a very inadequate mode of communication. Please resist the tendency, which I have noticed in myself as well, to project these inadequacies of medium upon the parties to the discussion. Brews ohare (talk) 15:13, 21 July 2008 (UTC)

I must admit, that was quite a fun question. I hope we have answered that to your satisfaction.- (User) WolfKeeper (Talk) 23:29, 22 July 2008 (UTC)

Wolfkeeper, you have just demonstrated to everybody that you can't see the difference between a rotating bucket of water in which the water climbs up the side walls, and a stationary bucket of water in which the surface is level.

You have tried to use specious mathematical arguments to convince us all that the two scenarios are exactly the same. David Tombe (talk) 01:39, 23 July 2008 (UTC)

The curvature of the bucket surface is the same, sure. I'm sorry if you believe that my argument that the energy is the same at all points on a surface that is flat to a gravity field is in some way specious.- (User) WolfKeeper (Talk) 02:19, 23 July 2008 (UTC)

As usual you guys are bashing David Tombe and treating him badly. That is your typical behavior. You act like the thugs which you are. You still need to apologise to him for your past bad behavior. You didnt do that so you have shown you are really not civilized people. I am still waiting for that apology to David, when are you going to do it???72.84.64.6 (talk) 13:19, 23 July 2008 (UTC)

High-handed activity by Editor Paolo

As noted under Talk:Centrifugal_force#Coordinate_systems_and_frames, Paolo has deleted a Note subject to question on this Talk page. He has repeatedly refused to discuss the validity of this disputed note, despite many examples and careful presentations by myself. His attitude is that he will eventually get around to discussing the matter, but it seems from his unwillingness to respond that may be some considerable time.

I would like to have an independent review of this matter. First, is there anything to dispute? As far as I can see Paolo hasn't got a leg to stand on. Maybe if he would explain himself, I could see he has a different perspective, but at present I just don't know what his objections can be. All we have so far from Paolo are some categorical, unsupported statements, and a refusal to engage in their discussion. Brews ohare (talk) 00:50, 21 July 2008 (UTC)

As explained here, the note was inserted by Brews and reflected his own opinion on a controversial topic still under discussion. This is not the first time that Brews tries to impose his own opinion before the end of a discussion. Last time he wanted to impose a figure which showed exactly the opposite of what was written in the text, and he was proven to be wrong. I have time to discuss only a topic at a time. As soon as Brews stops this edit war, I will be glad to discuss the specific topic, rather than Brews's behaviour. Paolo.dL (talk) 09:23, 21 July 2008 (UTC)

I see that Brews has not reinserted his note. Tonight or tomorrow morning, I will try and explain to Brews the reason why I am convinced his note is not compatible with what is written on physics textbooks, provided that Brews will not have reinserted it. Paolo.dL (talk) 09:38, 21 July 2008 (UTC)

Request for Comment (RFC)

• This debate has raged on and on up and down this page. My attempt to get everyone to calm down was ignored and refactored out of the discussion. I am opening this RFC in the hope that more users will participate in this debate and help bring it to a close. Beeblbrox (talk) 07:19, 21 July 2008 (UTC)

I apologize, Beeblbrox. Your comment was so generic, that I thought it did not refer to the specific subsection at the end of which you posted it. So, I inserted a section header above it. Please just remove it, or edit it, if you don't like it. You referred to original research, and the subsection at the end of which you posted your comment was about the behaviour of an editor who keeps trying to impose his own opinion by expressing it in the article, when only two opposite opinions (his an mine) are expressed in this page about that specific topic. Of course, one of us is wrong, but we both believe that what we maintain is consistent with the literature, not original research. I did not ignore your posting. I thought it referred to the debate about David Tombe's personal definition of centrifugal force. If your generic advice to "let go" was also addressed to me, I do not agree that we should leave on the article a note that provides a wrong definition of "frame of reference", a concept of central importance in this article. Paolo.dL (talk) 09:07, 21 July 2008 (UTC)

The debate: coordinate systems versus reference frames

I see from Paolo's remarks on "Talk:Frame_of_reference" that he has chosen to classify "coordinate system" and "frame of reference" as synonyms. Maybe that broad usage is acceptable in some contexts. However, the two are carefully distinguished in my Note, which is under dispute:

[Note: coordinate systems and frames of reference are independent. A frame of reference refers to the state of motion of the observer. A coordinate system refers to a choice of language used to describe observations. Any frame of reference can choose to employ any coordinate system (polar, elliptical, curvilinear, …) to describe observations in that system. A change in coordinate system does not mean a change in frame of reference, and vice versa.]

Apparently, though he somehow cannot formulate his viewpoint, even after days of deep deliberation, this is what Paolo wants to say:

"The term "frame of reference" is in general use in a less restricted sense than is conveyed in this Note".

It is amazing how Paolo cannot express himself on this simple, direct point, but can write pages of blah-blah-blah about "peers" and "editing responsibility".

I have rewritten the Note to make my usage of terms very specific and non-controversial. Here is the revised version:

[Note: coordinate systems and observational frames of reference are independent. An observational frame (such as an inertial frame or non-inertial frame of reference) refers to the state of motion of the observer. A coordinate system refers to a choice of language used to describe observations. An observational frame of reference can choose to employ any coordinate system (polar, elliptical, curvilinear, …) to describe observations in that system. A change in coordinate system does not change an observer's state of motion, and so does not entail a change in the observer's observational frame of reference, and vice versa.]

I'd be happy to hear from other editors whether they agree or disagree with this revised Note.

I also have introduced the modifier "observational" in front of "frame of reference" throughout the article, as its usage apparently cannot be inferred from context. Brews ohare (talk) 16:02, 21 July 2008 (UTC)

This is not "the debate", but Brews's inaccurate and biased version of the debate. Paolo.dL (talk) 10:25, 22 July 2008 (UTC)

I'm a previously uninvoled editor. To be honest, I'm have a really hard time following this debate. I don't see what the real dispute is. Is it a matter of source citing? Is one WP:RS contradicting another? I see that you've posted three proposed edits in this section. It seems to me that Paolo's edit is the one that includes WP:OR by saying "in general use". I should point out that neither of the edits listed here has any sources, so at this point, accusations by either side of WP:OR are undefendable.

Warning: There's no "edit by Paolo". All the versions of the note (that now became a section) were written by Brews. Paolo.dL (talk) 10:25, 22 July 2008 (UTC)

Assuming sources can be found to support the third proposed edit, I have some recommendations in regards to the actual wording. If I'm not mistaken, the difference between a coordinate plane and an "observational frame of reference" is the former always starts at the same point and in the same direction, and the latter is always relative...? I'm a math major and I'm having a hard time deciphering your meaning, that says something about the tone of the article I think. Additionally, the use of the word "obviously" in the last sentence is not only poor math writing (books with this word always frustrate people), but it violates words to avoid. I suspect including that word was meant more for Paolo's benefit than the readers'. AzureFury (talk) 16:57, 21 July 2008 (UTC)

Thanks for your interest. I think you are right about "obviously"; I'll remove it.

The point of this debate is to find a way to express the possible confusion between changing "state of motion" (for example, switching from an inertial frame to a non-inertial (that is accelerating) frame of reference, which has as one consequence the introduction of fictitious forces) and simply "changing coordinate system" (for example from Cartesian to cylindrical, which has no effect upon the presence or absence of fictitious forces). The confusion arises, for example, when a switch of coordinates is accompanied by a switch from inertial to non-inertial observational frames: there is a tendency of the mind that somehow identifies the two accompanied changes instead of keeping them distinct. Brews ohare (talk) 17:12, 21 July 2008 (UTC)

I have added several citations that, in my opinion, establish the viewpoint of this Note beyond all question. It is completely stupid to have wasted all this effort over an obvious point. Brews ohare (talk) 18:54, 21 July 2008 (UTC)

If a point is debated, the easiest way to stop wasting time is to reference it first. The less the point is worth arguing, the easier it should be to find a source. -- SCZenz (talk) 19:00, 21 July 2008 (UTC)

I hope that you are right. If every simple point required such reference, however, the article would consist of little else. Some reflection on the part of editors would avoid such silliness. Brews ohare (talk) 19:04, 21 July 2008 (UTC)

• Paolo, while I see your point in adding the header and I thank you and gladly accept your apology, clearly my advice to calm down and back away was not taken to heart. In the nine hours between my original post and the RFC poisting, there are about 65 edits to this page, mostly by you and Brews. Since the RFC started yesterday, there have been about 45 more edits to this page, again dominated by yourself and Brews. The purpose of RFC is to allow new, outside voices to enter the debate, not to keep re-hashing what has already been said, although the above summary could be helpful as this page is rather long. Anyway, please guys, Take a break. Beeblbrox (talk) 04:05, 22 July 2008 (UTC)

First of all, I believe the discussed note was not needed in this page. Brews just writes on the article whatever is discussed in this page. That's why this note was inserted. Not because it was necessary, but because it happened that we briefly discussed this topic in this page. And the more Brews wants to impose his opinion, the more the article grows in size: it was a useless note, and now it became a useless section.

Second, the new section still contains absurd sentences:

• "A change in coordinate system does not change an observer's state of motion". It certainly does, if the new coordinate system moves relative to the first one!
• "Coordinate systems and observational reference frames are independent". This is just a biased POV. For instance, two coordinate systems that rotate relative to each other, correspond to two totally different reference frames.

Moreover, I do not like the use of the word "observational" (is there a non-observational reference frame?). This is original and inappropriate terminology.

What I know about the difference between reference frame and coordinate system is explained in "Talk:Frame_of_reference" (I just added a reference). A year ago I posted there a note about the same topic. I think the discussion should continue there, where, by the way, Brews just rewrote the whole article according to his biased opinion!

Is it now clear to everybody what is the main problem here? Not the specific topic under discussion, but Brews's "one-man-band" attitude. Brews reinserted his questionable opinion on the article for the third time. He imposed his nonsense again before this discussion reached a clear conclusion. This is why I ask you to block Brews for a week, and remove the entire section from the article. Paolo.dL (talk) 09:48, 22 July 2008 (UTC)

The Note was added because Paolo did not understand the issue. He still does not. The Note's take on the issue is now documented by several citations.Brews ohare (talk) 10:50, 22 July 2008 (UTC)

You just confessed that you inserted your note into the article (about 200 words) just to explain your point to a single stupid editor, not to improve the article. Even if you were right, this would be a huge mistake. I keep asking others to help me. Brews will never listen to me. He needs to understand that articles are not his personal pulpit, and must be kept focused and readable. Paolo.dL (talk) 21:41, 22 July 2008 (UTC)

Your words, not mine: I said only you did not understand. Possibly other readers can benefit from this Note as well. Who knows? Brews ohare (talk) 22:45, 22 July 2008 (UTC)

ARGH

OK, you people are obviously not interested in looking for consensus on this issue. The core group of editors on this page seems to be content to argue with each other until Hell freezes over, meanwhile you accomplish nothing. The project is not well served by these never ending circular arguments. Beeblbrox (talk) 05:48, 23 July 2008 (UTC)

Hey, you may actually have a point here worth considering. What you guys need to do is ask yourselves what the user needs to know, and stop splitting fine points that the user will never understand. I give this article an F grade because it is not written for the user to understand but for wikipedia egos.72.84.64.6 (talk) 13:09, 23 July 2008 (UTC)

I do not agree about not looking for consensus. The subject has evolved; citations have been introduced. On Talk:Frame of reference I've rephrased the question as follows:

Our "debate" really seems to amount to a narrow specific issue: how one separates one procedure: the change from one state of motion to another state of motion; from the different procedure: the change of one coordinate system to another coordinate system while in the same state of motion. Do you have a way to express this distinction that you would endorse? Brews ohare (talk) 02:46, 23 July 2008 (UTC)

Maybe that will lead to consensus. Brews ohare (talk) 14:41, 23 July 2008 (UTC)

I agree that this article is stuffed with text which is useless for the reader. Particularly, the picky distincion between frame of reference and coordinate system. Reisnik and Holliday wrote an extremely successfull university textbook about mechanics without splitting hair about that distinction.

I appreciate Brew's effort to reach consensus. It is also true that he introduced interesting references. This discussion, however, does not belong in here (see Talk:Frame of reference) Paolo.dL (talk) 22:40, 23 July 2008 (UTC)

Some general comments on editing strategies

I've stopped keeping continuous track of this article, but it looks to me like there is still too much argument and too little sourcing. A very good example is the edit war over the difference between "reference frame" and "coordinate system"; it would be resolved much more easily by referring to a reference than by repeated addition and removal. There also seem to be flurries of editing over very minor points, which then end up overemphasized in the article--is it possible that, this being a general-purpose encyclopedia, we could resolve some of the arguments more concisely simply by being less specific? -- SCZenz (talk) 11:08, 21 July 2008 (UTC)

I was also surprised for the very long time needed to convince Brews that he was wrong about what I thought was an obvious detail (debated here and here). You might think that it was a debate about a trifling detail, but the figure that Brews wanted to impose, being a beautiful animation, was actually the most evident part of the article. I believe it is important to correct Brews's stubborn "one-man-band" attitude, which discourages me (and most likely others) from editing this article. I am ready to admit that I am wrong, when I am, as I already did above. I think it could be extremely useful if someone could help me to convince Brews that his behaviour is not compatible with Wikipedia policies. Up to now, he is still convinced that I am the devil and he is the exorcist (see just the title of this section). And I never failed to admit that Brews's numerous contributions are often very useful. The only problem is that, when his contributions are wrong or questionable, he is so much reluctant to admit they are, or at least admit they might be (before possibly proving otherwise), that he often does not even read the comments written to reach an agreement. In a different occasion, we were discussing a topic about which my position was neutral and others (mainly PeR) disagreed with him, and he did not even read the subject of a sentence of mine that he was summarizing (first sentence in this section). Paolo.dL (talk) 13:07, 21 July 2008 (UTC)

It has become clear that citations will not settle the matter. The distinction between inertial frame and coordinate system spelled out in the citations still appears to Paolo to be inessential. Brews ohare (talk) 10:55, 22 July 2008 (UTC)

I accept your references, but your own interpretation of them is incorrect. This point was already explained in Talk:Frame of reference. I know that you are intelligent, because of what you wrote before. But you keep attacking, rather than interacting, you want to prevail rather than discover the truth, and your summaries are biased. Thus, I deduce you have lost the capability of objective judgement, possibly due to excessive emotional involvement. You always fail to understand (or read) my explanations. And your misbehaviour has been producing damages, first in this article and then in Frame of reference. My only hope to correct you is with the help of others. You are never going to trust me. Only Rracecarr was able to convince you when you stubbornly refused to admit you were wrong about the giroscope precession figure. That's why I proposed to block you. I suffer for three reasons: I hate fighting this war, I hate doing that alone, but at the same time I perceive the extent of the damages you produced to the readability and reliability of this article and Frame of reference with your most recent edits. Paolo.dL (talk) 20:57, 22 July 2008 (UTC)

Hi Paolo: I am sorry to cause so much concern. My feeling is very similar to yours, but with you and I interchanged. Brews ohare (talk) 00:04, 23 July 2008 (UTC)

Citations are being ignored when it suits certain editors

The root cause of all the problems on these pages lies in the fact that centrifugal force is being treated as something that only occurs in rotating frames of reference.

I did applied maths and theoretical physics at university and I used the Goldstein's classical mechanics textbook as well as Williams's 'Dynamics'.

In both those books there are two quite distinct chapters in which the subject of centrifugal force emerges. There is,

(1) Rotating frames of reference. And,

(2) Planetary orbital theory.

Centrifugal force is a subject in its own right and it doesn't have to be studied exclusively in connection with rotating frames of reference. That is what is causing all the confusion on these pages. Every time a demonstration is introduced, they all have to start rambling on about looking at it from the inertial frame and looking at it from various rotating frames. They refuse to look at centrifugal force as a phenomenon in its own right.

I have tried many times to introduce planetary orbital theory unto the main page as a means of demonstrating centrifugal force. But those edits were instantly erased on every occasion, usually on the quite dishonest grounds that I hadn't supplied any citations when in fact I had.

The problem on these pages will not be resolved until a new independent group of administrators get involved and put the likes of RRacecarr and Wolfkeeper on a lead. At the moment, those two along with a few others have enjoyed a total liberty to delete the edits of anybody who they perceive to be contradicting their own prejudices, and the administrators that have been involved so far such as SCZenz and Anome have shown themselves to be totally biased.David Tombe (talk) 11:22, 22 July 2008 (UTC)

Point of agreement: "Centrifugal force is a subject in its own right and it doesn't have to be studied exclusively in connection with rotating frames of reference." However, I may not agree beyond this statement. Brews ohare (talk) 17:04, 22 July 2008 (UTC)

You did not reply to this item, copied from above (with an additional question):

Hi David: So the long and the short of it is that two bodies, both moving in straight-line motion relative to the fixed stars, but in paths that are skew (i.e. are neither parallel nor intersecting) will exhibit both tangential motion and also centrifugal force. Is that your statement? Assuming the answer is "yes", do both bodies experience this force, and is it equal and opposite for each? Is the force seen in the frame of the fixed stars, or only on the inertial frame attached to one or the other body? Brews ohare (talk) 22:23, 20 July 2008 (UTC)Brews ohare (talk) 17:07, 22 July 2008 (UTC)

Brews, the answer is 'yes'. And the scenario is even more general than you have stated. It applies to any mutual motion other than when the two particles are on a collision course (or an ex-collision course). And the centrifugal force can be observed from any reference frame. The effect is reference frame independent. It will be observed as a radial acceleration. Ie. the two particles will be accelerating apart from each other based on the line that joins the two particles. Mutual tangential motion will always have an assocaited outward radial acceleration given by rω^2, and contrary to what Paolo.dl says, this is the definition of centrifugal force that is used in both planetary orbital theory and in rotating frames of reference theory.

And the effect will act equally and oppositely on each particle.

However, if one of the particles is only an imaginary point, then the effect will be mathematically real but without any physical reality. David Tombe (talk) 01:30, 23 July 2008 (UTC)

To pursue this matter of two objects in straight-line motion. As both experience (in your view) a centrifugal force, I'd assume that they will not continue to follow a straight=-line path, according to Newton's second law. So it begins to sound like Newton's first law is not part of your thinking?? It is basically impossible to realize straight-line motion when there are no "real" external forces around if there are two or more bodies in the universe.?? Brews ohare (talk) 03:24, 23 July 2008 (UTC)

Centrifugal and reactive centrifugal force

David, possibly you confuse the fictitious "centrifugal force" with the real "reactive centrifugal force". You cannot judge all the other editors as biased, when you still adopt a personal definition of centrifugal force that is not compatible with the widely accepted definition given in this article (see above). Paolo.dL (talk) 20:23, 22 July 2008 (UTC)

Paolo.dL, I'm fully aware of the distinstion between the different kinds of centrifugal force including what you term reactive centrifugal force. I am most certainly not confused in that respect. Any satisfactory article about centrifugal force will ultimately have to detail all these different phenomena which come under the umbrella heading of centrifugal force.

So far I have not been getting heavily involved in debating these kinds of details.

The definition of centrifugal force as is given in this article is quite wrong. Centrifugal force is not defined exclusively in connection with rotating frames of reference. I can give you at least two quality citations from university textbooks which deal with rotating reference frames in one chapter and lead up to what they describe as the 'well known centrifugal force'. In other words, centrifugal force is something that is already understood and defined independently of rotating frames of reference.

This is corroborated by the fact that the same 'well known centrifugal force' is then mentioned again in another chapter on planetary orbital motion in a context which does not involve rotating frames of reference.

In fact orbital theory uses polar coordinates in the inertial frame.

I am finding it difficult to accurately follow your argument with Brews. It seems to me that you are arguing about coordinate frames and coordinate systems. I believe that the confusion is totally connected with the fact that matters to do with centrifugal force as would normally be dealt with using polar coordinates, are being dealt with in the article within the totally unsuitable context of rotating frames of reference.

While I was blocked in June, a new editor called TstoneT appeared. He seemed to be arguing what I am saying, that polar coordinates can be used to deal with centrifugal force independently from rotating frames.

But TstoneT has now disappeared. Nevertheless, TstoneT's comments hit a raw nerve with Wolfkeeper who stated that the article is about rotating frames and that he has no intention of changing that. Wolfkeeper has also stated in strong terms that this article is not about polar coordinates.

Wolfkeeper has got absolutely no right, or no basis in the textbooks, to demand that centrifugal force must be treated exclusively in connection with rotating frames of reference. But you will notice that there is a hierarchy amongst the group of editors here that control the article. Nobody ever crosses Wolfkeeper. Nobody crosses RRacecarr either, but not even RRacecarr will ever cross Wolfkeeper. The administrators always back up Rracecarr and Wolfkeeper.

LOL. I wish.- (User) WolfKeeper (Talk) 02:12, 23 July 2008 (UTC)

Actually I claim no such thing. I claim that this article is about rotating frames of reference. I absolutely don't deny that things sometimes called centrifugal forces and coriolis forces can exist in polar coordinates, but they're different. And I'm not in any way opposed to them being described in the wikipedia. I just don't think that this is the right article to do that; if nothing else it's big enough already. If you want to create another article on polar centrifugal force, go right ahead David. Centrifugal force (polar)?- (User) WolfKeeper (Talk) 02:12, 23 July 2008 (UTC)

Wolfkeeper, that's exactly where you've got it all wrong. This article is about centrifugal force. It is not about rotating frames of reference. David Tombe (talk) 02:24, 23 July 2008 (UTC)

No, it really isn't, and this is probably why you are having so many problems with everyone here. If you do a search on 'centrifugal force' in google, and read the articles that come up carefully, they almost all describe non inertial frames of reference (i.e. rotating reference frames), and the wikipedia is just the same. Centrifugal force and coriolis force in polar coordinates is perfectly valid, but not quite the same. Just because they are called the same term, doesn't mean that they are the same thing. Centrifugal force in polar coordinates is always radial, and coriolis is always transverse- this is not the case in non inertial frames of reference where coriolis is always perpendicular to the velocity vector (and the velocity vector can point in any arbitrary direction at all). This seems to be the source of your confusion.- (User) WolfKeeper (Talk) 02:49, 23 July 2008 (UTC)

Wolfkeeper, the title of the article is 'Centrifugal Force'. And on that other point, Coriolis force in polar coordinates is clearly a tangential effect. There is no confusion on my part. The confusion lies with he textbooks that treat Coriolis force as purely tangential when it comes to polar coordinates and planetary orbits, but then allow its direction to be arbitrary when it comes to dealing with rotating frames of reference.David Tombe (talk) 03:02, 23 July 2008 (UTC)

Until that state of affairs is altered, the situation doesn't look very hopeful. David Tombe (talk) 01:12, 23 July 2008 (UTC)

Once more to make this very clear to you guys. The user is going to enter centrifual force, he is not going to know the difference between this and reactive centrifugal force. So this article will be useless to him because it doesnt discuss what he is seeking information about. You need to combine the articles and explain the difference in the one article. Otherwise you are confusing the user.72.84.64.6 (talk) 13:12, 23 July 2008 (UTC)

Wolfkeeper wikistalking again

I made an edit to the introduction which in normal circumstances shouldn't have needed a reference because it is uncontroversial. Nevertheless I decided to put a reference in for good measure. Within five minutes of having made the edit, and while I was in the process of typing in the reference, Wolfkeeper in his normal style swooped in and deleted the edit. David Tombe (talk) 02:03, 23 July 2008 (UTC)

You've reinserted it, but I'm very inclined to remove it again. The reason is not that it's wrong, but it's too specific. The first thing in any article is supposed to be a definition, and I don't think that centrifugal force is in any way specific to planetary motion (but I in no way disagree that it does appear in many equations that you can write for planetary motion.) I just disagree that we should define it as something that is found there, as opposed to everywhere else it's also found.- (User) WolfKeeper (Talk) 02:40, 23 July 2008 (UTC)

Wolfkeeper, the introduction does not define centrifugal force at all. As it stands now, the introduction states two major theoretical physics/applied maths topics in which centrifugal force is treated, and it gives a brief description of the effect in each case.

Nothing at all regarding rotating frames has been removed from the introduction.David Tombe (talk) 02:59, 23 July 2008 (UTC)

When we define something in the wikipedia we define what it is for the article. A different definition goes in a different article. That's the main difference between a dictionary and an encyclopedia article- an encyclopedia only treats one subject/topic per article and has multiple articles if there are multiple definitions.- (User) WolfKeeper (Talk) 03:45, 23 July 2008 (UTC)

This is the most stupid ridiculous answer I have even read. The user doesnt enter reactive centrifugal force he enters centrifugal force. Thus he gets the wrong page, because your definition ignores what the user is thinking. This is why you guys are creating a web site that users find stupid and poorly written. You need to stop writing articles that feed your own egos, and start writing articles that users really can use. They dont care about your ego trips here in the wikipedia dream world. They want information that they can understand and use. You get an F grade on that score.72.84.64.6 (talk) 12:59, 23 July 2008 (UTC)

Centrifugal force and tides

This is a sticky subject. There are many influences on the tides. A principle influence is the tidal force which has nothing to do with centrifugal force, but has to do with the gradient of the Moon's gravitational force. The radially outward component of this tidal force appears to be less significant than its tangential component. In addition, the centrifugal force that is operative is the centrifugal force due to rotation about the barycenter, not the about the Earth's axis of rotation. Thus, bringing this matter up is a dubious exercise as it is not a clean example of centrifugal force, but requires a great deal of background. As it is, the article on tides is a total mess and cannot come to grips with the issues involved. I'd recommend that no mention of tides be made. Brews ohare (talk) 02:56, 23 July 2008 (UTC)

It does contribute though, we should probably mention it; but we don't have to make a big deal of it.- (User) WolfKeeper (Talk) 03:42, 23 July 2008 (UTC)

What does it contribute? Confusion? It does not seem to add to our understanding to suggest that centrifugal force is a murky contributer to a murky subject. Brews ohare (talk) 03:44, 23 July 2008 (UTC)

Here is a little discussion to point out what we are getting into here:

Why aren't the Atlantic and Pacific coast tides the same?

"The nature of tides on the Earth's oceans is very complex. The oceans are, of course, being periodically 'forced' by a number of tidal sources including the Moon and the Sun, but this forcing has a number of different periods and harmonics. The two dominant periods are sue to the Sun and Moon, these are referred to as the S1 and M2 'modes' which have roughly 12 hour periods because they raise TWO water tides on the ocean diametrically opposite each other. But, for a variety of reasons, any given port will not have two high and two low tides each day; also called 'semi-diurnal tides'. A careful monitoring of the tides at any port for several years will show that in addition to the major modes, there are as many as 300 minor or 'harmonic' modes as well.

The World Ocean is a complex dynamical system. The natural velocity of a water disturbance depends on the depth and salinity of the water at each point it passes. When bodies of land circumscribe bodies of water, they produce a collection of resonating systems that favor water oscillations with certain frequencies over others. From among the 300+ harmonics that can be measured, every port and coastal location has its own unique signature depending on its latitude, longitude, water depth and salinity. The result is that the 'two high two low' tide rule can be strongly modified so that the time between successive high tides can be greater than or less that 12 hours in many cases. The result is that for some locations, there can be days when only one high tide occurs. Looking at the Atlantic and Pacific Coast tide tables for 1995, the data for the various 'Standard Ports' showed that virtually all days had two high tides and two low tides in San Diego, San Francisco, New York and Charleston. There were, however a few days every few months when only a single high tide occurred." - Dr. Odenwald's ASK THE ASTRONOMER

Brews ohare (talk) 04:14, 23 July 2008 (UTC)

Figure 9: Lagrange points

Inadequate links and discussion of this figure. How does the figure contribute to the understanding of the article? As it stands, it does not contribute. A description of Lagrange points has not been attempted and might lead the reader far off topic. Without more context, this figure should be deleted. If necessary context is too large, it also should be deleted. Brews ohare (talk) 03:15, 23 July 2008 (UTC)

It's one of the most important uses of rotational reference frames in physics, and the diagram shows the potential energy due to the centrifugal force (in conjunction with gravity).- (User) WolfKeeper (Talk) 03:37, 23 July 2008 (UTC)

I'd suggest adding some discussion in the text proper to explain (i) definition of Lagrange point as a point where a massless object remains stationary, and (ii) what does this example tell us about centrifugal force anyway? The article on Lagrange point uses centripetal force instead. Is there anything we should know about this switch of view? Why are we using a non-inertial frame, for example? Brews ohare (talk) 03:43, 23 July 2008 (UTC)

Sigh. Strike for the centripetal heads then. The L4 and L5 Lagrange points are only stable due to coriolis forces (or that's how it's normally analysed), and the potential energy graph is due to the centrifugal force not the centripetal, and these points are only stationary in the rotating frame of reference.- (User) WolfKeeper (Talk) 13:41, 23 July 2008 (UTC)

No, they cover both non rotating and rotating frames of reference in the introduction, and the diagram is in the rotating frame.- (User) WolfKeeper (Talk) 13:44, 23 July 2008 (UTC)

Wolfkeeper, the potential energy due to centrifugal force in a gravitational field exists as a matter of fact without involving rotating frames. There's a whole page on it in Goldstein's (page 78). Centrifugal potential energy in a gravitational field is obtained by substituting Kepler's areal constant into the expression for kinetic energy and obtaining a position dependent term (inverse square law to be precise, which means that centrifugal force in a gravitational field is an inverse cube law repulsive force).

Why is it, everybody else here is talking about centrifugal force being a vector, whereas for you it's a scalar? Why is everybody else talking about rectangular coordinates whereas you are talking about polar? Why David? Why do all major sources use rectangular, whereas you can, at best find a few obscure references here and there? This topic is different to what you are talking about.- (User) WolfKeeper (Talk) 13:41, 23 July 2008 (UTC)

In the example given in the centrifugal potential energy section in this wikipedia article, prior to you introducing the three body problem, we are dealing with the conversion of rotational kinetic energy into other forms of potential energy. The example of the rotating water is in fact a reactive centrifugal force example in which the potential energy is associated with the pressure caused by the centripetal force that forces the water off its inertial path. It is also a point in fact however that tangential kinetic energy (or for that matter, rotational kinetic energy) is in fact the same thing as centrifugal potential energy. So the example involves centrifugal potential energy being converted into gravitational and hysrostatic potential energy.

Interstingly, if you agree with Maxwell's theory of magnetic repulsion which employs centrifugal force, then it becomes clear that magnetic repulsion does not obey the inverse square law. On summation over his molecular vortices, it may not even obey the inverse cube law. But at any rate, it becomes quite clear why we can have magnetic levitation. Earnshaw's Theorem should not be involved when considering magnetic levitation. Hence there should be no controversy.

Based on Maxwell's works, we can deduce that magnetic potential energy is in fact fine-grain centrifugal potential energy. Does that help to explain why we can have a magnetic potential energy when in fact the force law that is used to explain electromotive force, F = qvXB, allegedly has got no associated potential energy?

And does it help to explain why I deleted the bits that RRacecarr restored?

Remember, Coriolis force and the F = qvXB force are mathematically identical if not physically identical.

I'm seriously considering that Coriolis force and F = qvXB do have an associated potential energy, and as in the case of centrifugal force, it is given by grad (A.v). Goldstein's backs me up on this. In the Lagrangian chapter at page 23, they derive A.v as a Lagrangian for the F = qvXB force. And there is some on-line encyclopaedia (something like Eric Weisstein) that writes the Lorentz force using grad (A.v) for the vXB term.

But in order for it to make any physical sense, we would have to involve vorticity. In the absence of vorticity, Coriolis presure/potential energy would have to be externally applied such as would be the case in water moving radially along a pipe on a rotating turntable.

In fact, I think that we should move all references to potential energy in connection with Coriolis force off these pages completely and unto the Coriolis page page, as the matter is highly controversial. David Tombe (talk) 13:10, 23 July 2008 (UTC)

Wolfkeeper is a wikistalker

Wolfkeeper, you are a wikistalker. You are messing the whole article up out of sheer spite. We need one centrifugal force article. This article is not about rotating frames. It is about centrifugal force.

Planetary orbits are thee single most important example of centrifugal force. They determine the inertial path.

You are making a dog's dinner out of it all. You are bringing in alot of unnecesary complications about three body problems into the potential energy section while at the same time deleting all references to the two body problem.

This is because you can't understand the two body problem. Nobody can understand the three body problem and that is why you like to hide behind the three body problem. David Tombe (talk) 14:21, 23 July 2008 (UTC)

Your continued personal attacks sadden me David. You have already been banned for a month because of these things.- (User) WolfKeeper (Talk) 14:29, 23 July 2008 (UTC)

Wolkeeper sends for the troops. FyzixFighter arrives duly on scene

Now we are seeing the mechanisms very clearly. In order to prevent Wolfkeeper breaching the three revert rule, his ally FyzixFighet takes over. No discussion whatsoever. FyzixFighter deletes perfectly good sourced material for the sole purpose of backing up Wolfkeeper.

And the administrators let all this happen. Until such times as Wolfkeeper, RRacecarr, FyzixFigher, PeR, SCZenz, Anome, Itub, Plvekamp, and Henning Makholm are put on a tight lead, this article well remain a total dog's dinner. David Tombe (talk) 14:27, 23 July 2008 (UTC)

Whatever your theories about editor conspiracy, David, this revert was beneficial because your statement, while valid, was not a general statement but a statement specific to planetary motion. In the Intro the present general statement, which also applies to planetary motion, is appropriate. Brews ohare (talk) 14:30, 23 July 2008 (UTC)

My reason for the revert was your blatant disregard for WP:3RR. However, now that I've had a chance to look up Goldstein, I believe that your statement is a misrepresentation of what Goldstein is actually saying (taken from the 2002 edition - couldn't find the 1980 one) concerning the central force problem and orbits:

The equation of motion in r, with ${\dot {\theta }}$ expressed in terms of l, Eq. (3.12), involves only r and its derivatives. It is the same equation as would be obtained for a fictitious one-dimensional problem in which a particle of mass m is subject to a force $f'=f+{\frac {l^{2}}{mr^{3}}}$. The significance of the additional term is clear if it is written as $mr{\dot {\theta }}^{2}=mv_{\theta }^{2}/r$, which is the familiar centrifugal force.

Note that Goldstein only introduces centrifugal force when the orbit equation is reduced to a fictitious one-dimensional problem. A little later in the book (pg 176 in the 2002 edition), Goldstein is a little clearer of what the fictitious one-dimensional problem means and addresses your argument a little more directly:

If we analyze the motion of the Sun-Earth system from a frame rotating with Earth, it is of course just the balance between the centrifugal effect and the gravitational attraction that keeps the Earth (and all that are on it) and Sun separated. An analysis in a Newtonian inertial frame gives a different picture. As was described in Section 3.3, the angular momentum contributes to the effective potential energy to keep the Earth in orbit.

--FyzixFighter (talk) 19:13, 23 July 2008 (UTC)

FyzixFighter, You have admitted that you made the reversion before you had even studied the details. Your excuse about the three revert rule was nonsense. How could I have broken the three revert rule without Wolfkeeper also having broken it? That was a total rubbish reason.

Your prejudice means that nothing that you say above can be taken seriously. You have simply adopted the usual stance which you guys do when you are confronted with citations that contradict what you have been saying. Just as you denied the GD Scott reference and just as SCZenz. PeR, and Anome denied the Maxwell reference, you are playing the old trick of pretending that you see a different meaning in the reference.

It's quite clear to all unbiased observers simply from what you have written above, that centrifugal force is involved in central force orbits without recourse to rotating frames of reference. Your attempts to try and pretend that Goldstein meant otherwise were pathetic. It's just a pity that there aren't any administrators who can see right through the likes of you. David Tombe (talk) 21:21, 23 July 2008 (UTC)

Actually, I think it's quite clear that Goldstein is saying that the centrifugal force only arises when considering central force orbits in rotating frames of reference. Where does my analysis of Goldstein's statements go awry? I provided the full quotes above so that others can look at the Goldstein quotes above and determine for themselves. You, David, argue that Goldstein supports the idea that the centrifugal force is real and independent of a rotating frame. I argue that in both the quotes, he limits the use of the centrifugal force to rotating frames - implicitly in the first quote (mapping to a fictitious one-dimensional problem is equivalent to a frame rotating with the Earth) and explicitly in the second quote. I gladly invite any admin and editor to look at the quotes and see which is the correct representation of Goldstein. --FyzixFighter (talk) 21:47, 23 July 2008 (UTC)

And by the way, you are continuing to break WP:3RR with your edits removing the coriolis force-potential energy comment. From that policy's page "An editor must not perform more than three reverts, in whole or in part, on a single page within a 24-hour period. A revert means undoing the actions of another editor, whether involving the same or different material each time." I would like to assume that you are not aware of that small caveat, and would encourage you to self revert. --FyzixFighter (talk) 21:55, 23 July 2008 (UTC)

FyzixFighter, there is nothing at all about rotating frames in that chapter. You jumped ahead to another chapter to draw your references to rotating frames.

The matter is clear cut. Centrifugal force appears in the orbital equation and there is absolutely no need to involve rotating frames. It is exactly as I said to you a while back. It is a scalar equation in the radial direction and the mv^2/r term is centrifugal force. I recall that you had previously tried to argue that the mv^2/r term was referring to centripetal force, and somebody else was trying to tell me that it was a vector equation. I think that person was maybe SCZenz.

There is absolutely no basis for the present introduction which implies that centrifugal force is something that only arises in connection with rotating frames.

You deleted a sourced sentence which clearly indictated that centrifugal force is an outward force which occurs in planetary orbits. David Tombe (talk) 01:20, 24 July 2008 (UTC)

Straight-line motion in inertial frame

David: Can you divert yourself from engagement in the social heirarchy of Wiki to answer this question asked earlier:

To pursue this matter of two objects in straight-line motion. As both experience (in your view) a centrifugal force, I'd assume that they will not continue to follow a straight=-line path, according to Newton's second law. So it begins to sound like Newton's first law is not part of your thinking?? It is basically impossible to realize straight-line motion when there are no "real" external forces around if there are two or more bodies in the universe.?? Brews ohare (talk) 03:24, 23 July 2008 (UTC)

They will continue to follow a straight line path unless a centripetal force acts. That's the principle of planetary orbits. The centripetal gravity force and the centrifugal repulsion force act together in tandem.

As centrifugal force falls off on an inverse cube law, gravity takes over and pulls the object back again. It speeds up and the tangential motion increases. Eventually it hits the centrifugal repulsive barrier (terminology straight out of page 78 of Goldstein's) and it starts to go back out again.

By the way, why have tides suddenly been introduced to the centrifugal potential energy section? That is so typical of the nonsense that is going on here. Completely erase all references to centrifugal force where it really occurs, such as in the two body problem, and then introduce it into a topic where it is irrelevant such as the tides. Centrifugal force is in the oceans, tides or no tides.

That sums the whole mess up. All those who can't handle the two body problem, hide behind the three body problem in order to pretend that they know what they are talking about. David Tombe (talk) 17:26, 23 July 2008 (UTC)

David: You are confusing me about what you really think about the two objects in straight-line non-intersecting motion in an inertial frame fixed to the fixed stars. On one hand, you have said that two such bodies in straight-line motion do exhibit tangential motion and will be subject to centrifugal force. Now you say they will be subject to centrifugal force only if they are also subject to centripetal force. But ... I cannot see any centripetal force occurring unless the objects are in a curved path. So, you can see my dilemma. What do you want to say?? Brews ohare (talk) 21:18, 23 July 2008 (UTC)

Brews, I'm only trying to teach you textbook orbital theory. It deals with centrifugal force and it defines centrifugal force.

Centrifugal force in the absence of centripetal force will result in straight line motion. If we add centripetal force, then we will get curved path motion.

Gravity is a centripetal force. If we add it to centrifugal force, the result depends on the relative magnitude of the two opposing forces.

At the extreme end with centrifugal force only, we will have two straight lines. These are the limiting cases of infinitely eccentric hyperbolae.

Increase the centripetal force and we will get hyperbolae.

Increase it more and we will get parabolae.

increase it more and we will get elliptical closed orbital motion.

At the other extreme, when there is no centrifugal force and only centripetal force, we will have straight line radial motion. The two particles will come together on a collison course.

We do not need to involve rotating frames in order to study centrifugal force. Centrifugal force is a topic which crops up when we study rotating frames. You were wrong to back Wolfkeper on his reversion of my sources edit. David Tombe (talk) 21:36, 23 July 2008 (UTC)

David: I am not talking rotating frames here. I'm talking straight lines. You say:

Centrifugal force in the absence of centripetal force will result in straight line motion.

But in the inertial frame of the fixed stars, straight-line motion means no net force. So how can there be centrifugal force?? There is nothing to balance it, to make zero net force, because there is only one other body, also in straight line motion. The only force that body generates is centrifugal force. Sounds impossible ?.! Brews ohare (talk) 00:46, 24 July 2008 (UTC)

Brews, in an inertial frame of reference two objects in straight line motion may well have no acceleration as regards the X, Y and Z directions. But they will still have a mutual acceleration in relation to the line that joins them together.

I may well be getting blocked soon. If you are genuinely interested in this topic, get my e-mail address and we can discuss it by e-mail. You have some fixed ideas which are blocking your ability to achieve a greater understanding. One of your problems is an absolute insistence on trying to view everything in terms of X, Y, and Z. David Tombe (talk) 01:36, 24 July 2008 (UTC)

David: I gather the X, Y , Z directions are in the frame of the Fixed Stars. Thus, zero acceleration is seen in this frame. As it is an inertial frame, that means there are no net forces on these objects in any other inertial frame. Therefore, the mutual acceleration that you refer to "in relation to the line that joins them together" implies a choice of a different frame that is a non-inertial frame. Your discussion of this example is therefore incomplete, in my view, because you have introduced new frames of reference without saying what they are. Moreover, this non-inertial frame is not attached to either of the objects, as they are moving at constant velocity and so also are in inertial frames. Brews ohare (talk) 21:50, 24 July 2008 (UTC)

Brews, we don't need to introduce frames of reference at all to discuss centrifugal force. If two points possess mutual tangential speed relative to the background stars, then they will automatically possess an outward radial acceleration. The second time derivative of the distance between the two particles will be v^2/r where v is the mutual tangential speed and r is the distance between the two particles.

It is as simple as that. That is the very centrifugal force that is used in the analysis of planetary orbital motion. David Tombe (talk) 18:53, 25 July 2008 (UTC)

David: No need for any coordinate frames: the objects are in uniform straight-line motion relative to the fixed stars. Therefore, there is no net force upon them. There are no sources of force other than each other. We are assuming their gravitational interaction is not a factor (small mass and/or large distances). There isn't any force, centrifugal or otherwise, not in the frame of the fixed stars nor in any other inertial frame of reference. That is my version of "as simple as that". Brews ohare (talk) 23:46, 25 July 2008 (UTC)

Brews, I have my own theories on it which can't go on these pages. But irrespective of those theories, the facts are clear cut. There really will be a radial acceleration given by v^2/r. That is an undeniable fact. I admit that it is a curious fact and I can see why there may be a tendency to write it off as being merely an incidental geometrical fact and that there is no underlying active push force present.

I have pondered it for years. But then try and extrapolate it to the case of two central force orbits (four particles) side by side in their mutual equatorial plane. That's a scenario which we seldom encounter on the large scale. Nevertheless, Maxwell used that principle to account for magnetic repulsion using centrifugal force.

I'll tell you this much. I believe that the v^2/r acceleration between the two particles in question does indeed have a physical cause which is highly connected to both gravity and the background stars.

But meanwhile, I need you to come face to face with the undisputable fact, irrespective of the cause, that two particles moving in straight line motion will experience a mutually outward radial acceleration given by v^2/r where v is the mutual tangential speed and r is the distance between the two particles.

And if you read Goldstein's or indeed any university applied maths textbook, you will see that this is exactly the expression that is used for centrifugal force and centrifugal potential energy in planetary orbital motion. And in conjunction with gravity, it leads to elliptical, parabolic, or hyperbolic orbits.

At the moment, all fully sourced references to centrifugal force in relation to planetary orbital motion are being deleted from these pages under the noses of the administrators. David Tombe (talk) 10:51, 26 July 2008 (UTC)

David: It appears that you are going to have to say straight-out at this point that Newton's laws are incorrect. The only alternative is to address my point above, and explain how your views are compatible. 71.80.210.217 (talk) 17:04, 26 July 2008 (UTC)

Brews, I agree with Newton's three laws of motion absolutely. But I think that they are better expressed in the singular form of Mach's definition of inertial mass. Mach said that the mass is inversely proportional to the induced accelerations associated with mutual interaction. In other words m1a1 = -m2a2. That is Newton's three laws all in one.

There is nothing that I have said above that contradicts Newtons laws. But I think I know what you are thinking. You see straight line motion in an intertial frame and you think of inertia and Newton's first law. You think that no forces are acting and that there is no acceleration. Then here comes me telling you that there is a centrifugal force acting radially outwards between the two particles.

Actually, my disagreement with Newton is over the issue of the existence of this centrifugal force. But if it does exist then it causes a centrifugal acceleration and hence it doesn't breach Newton's laws of motion.David Tombe (talk) 21:37, 26 July 2008 (UTC)

I think there's some misunderstanding there. David begins by assuring us that he agrees with Newton's laws absolutely, but ends by saying he disagrees with Newton over the existence of a net centrifugal force on an object that is moving inertially. Needless to say, this is in direct contradiction to Newton's laws, so something is obviously amiss in David's thinking. From his other comments, it seems that he actually rejects the whole premise on which Newtonian mechanics is based, which is the principle of inertia. David apparently wishes to advocate some kind of purely relational theory of motion, of the sort that Leibniz, Berkeley, Mach, etc., dreamed about. In such a theory, inertial coordinate systems are just an emergent aspect of a physics that ultimately depends only on the pairwise distances between particles. However, even if we disregard field phenomena, no fully consistent theory of particle mechanics based on the relational principle has ever been formulated (and there are many compelling reasons to believe that no such theory CAN ever be fully consistent). In any case, David's comments are all in the category of "novel narrative". According to Newton's laws (with which David says he agrees), the acceleration of an object is NOT defined as the rate of change of the distance between that object and some other object. It is defined as the rate of change of the particle's inertial coordinates x,y,z with respect to the time coordinate t. This is the definition of "acceleration" in terms of which Newton's laws are formulated. It is invalid to say that we agree with Newton's laws but then to propose to re-define the parameters appearing in those laws. Obviously we can transform any law into any other law simply by re-defining the terms. This is what David is trying to do, and this explains his self-contradictory claims to both agree with Newton's laws and to disagree with Newton. The meaning and content of a physical law depends on the meanings of the terms used in the expression of that law.

In summary, I think if all the editors agree to stick to accepted physical theory, and not try to introduce their own novel narratives and relationalist notions, the editing of this article would be much more straightforward. Perhaps David would like to devote himself to creating an article on relational theories of motion? If he does, I would urge him to first acquaint himself with the history of the subject, and understand the reasons for the predominance of theories based on the principle of inertia rather than the principle of relationism.63.24.120.84 (talk) 19:33, 27 July 2008 (UTC)

63.24.120.84, That was a pretty good analysis of my position. It's absolutely true that I have never been happy with the Newtonian concept of the inertial frame of reference and X,Y,Z. As I said above, I much prefer Mach's approach. I do see your point that my application of Newton's laws to a force in the radial direction is at variance with Newton's law of inertia in X,Y,Z. But then of course that applies to the centripetal force just as much as to the centrifugal force. One of my biggest problems during the height of this edit war was that my opponents would use polar coordinates for their arguments but then switch into X,Y and Z in order to sabotage centrifugal force. My argument was that planetary orbital theory is done exclusively in polar coordinates. My opponents have consistently refused to allow any mention of that topic in the main article despite my having provided very good references from standard university textbooks. In my mind, centrifugal force is the same thing as inertia but described in a different language. The logic that my opponents were using in order to deny the existence of centrifugal force was equivalent to saying that aeroplanes don't exist because in German we call it a Flugzeug. In summary, I fully support the principle of Newton's laws of motion but even to the extent of extending them into polar coordinates. If that makes me at variance with Newton's original intentions, then Brews does indeed have a point. But the modern classical mechanics textbooks are also at variance with Newton's approach to planetary orbital motion for that very reason and I was basing my own approach entirely on how I learned it at university through Goldstein's etc. I am not advocating any original research as regards centrifugal force on these pages. I am glad however to see that you have been able to identify the issues because few others have. There is another anonymous that seems to have identified the issues, and there was a username TstoneT who came here briefly in June. I think that he was on the right lines too and he suppplied some references regarding dealing with centrifugal force in polar coordinates in what he called the inertial frame. At the time, he disagreed with me but it was because of a misunderstanding regarding him talking about stationary polar coordinates in the inertial frame. His terminology confused me but I realize now that he was talking about polar coordinates and the fact that centrifugal force was a radial force. On the issue of original research, I do do original research. You said that a Machian approach had never been completed and that I should enquire into why. I have been working hard on decyphering Maxwell's molecular vortices and linking centrifugal force to magnetic repulsion. I haven't as yet encountered any problems with the particle to particle approach. Can you give me any summary of where it is believed that such an approach breaks down. David Tombe (talk) 01:36, 28 July 2008 (UTC)

Article talk

Until now, I've largely ignored the discussions on this page, as it appeared that nothing terrible was happening to the article and no edit wars were breaking out. I do think that the participants in the discussion are having a general discussion about physics rather than a discussion about how to improve the article using sourced, properly referenced materials from standard texts, which is what everybody's supposed to be doing on Wikipedia. Disparaging remarks have no place here, nor does original research or analysis. This article is the subject of informal mediation as noted at the top of the page, and I strongly urge that everybody avoid endless philosophical discussion and complaints about other editors. Acroterion _(talk) 14:47, 23 July 2008 (UTC)

Acroterion, you saw for yourself that I put in a fully cited paragraph in the introduction to the extent that planetary orbital theory was a topic that was just as relevant to centrifugal force as rotating frames of reference.

It was deleted by Wolfkeeper and FyzixFighter. If the situation had been reveresed, I would have been blocked by now for having removed cited material.

You have seen that Wolfkeeper thinks that this article is about rotating frames of reference when in fact it is clearly about centrifugal force.

Your complaints above mean absolutely nothing. It has been shown over the last few months that it takes very little for me to be blocked.

If you think that there is something wrong going on on these pages, then let's see you blocking somebody. A general complaint directed at nobody in particular doesn't solve anything.

Let's see you blocking Wolfkeeper and FyzixFighter for wikistalking and removing sourced material. David Tombe (talk) 17:18, 23 July 2008 (UTC)

You were blocked for attacking other editors. You are engaged in an editing dispute, and I have suggested already that all parties confine themselves to working out the dispute rather than talking past each other, demanding disciplinary action and compiling lists of opponents. This is not a controversial topic - we have articles on Palestine and Ireland with less conflict. The talk page has become a debating society. The remedy for removal of sourced information in an edit war is to protect the article page in The Wrong Version, whatever that may be, not to block editors. Acroterion _(talk) 18:30, 23 July 2008 (UTC)

Yes Acroterion, on the last two occasions, I was blocked for supposedly being uncivil to other editors following severe provocation. The provocation came from Wolfkeeper who was blatantly wikistalking. He broke all the rules. Meanwhile, SZCenz hung around waiting for me to show the first signs of anger and then he blocked me for one month.

I haven't noticed any of them ever getting blocked for being equally uncivil.

On the previous occasions, I was blocked on the basis of downright lies on the part of administrator Anome.

Anyway, I hope you live up to your word. I'm soon going to re-install the sourced sentence about centrifugal force in planetary orbits. I'll be looking forward to seeing you locking the page.

If you are genuine and you read what FyzixFighter wrote above, I think you will begin to understand what this edit war is really about.David Tombe (talk) 21:25, 23 July 2008 (UTC)

No, the system is not to be gamed like that. The article is protected as it stands, and I am uninterested in whose version it reflects. Any repetition of the above comment concerning "lies" aimed at any other editor on the wiki will result in a lengthy block. Work it out on the talk page. Acroterion _(talk) 23:05, 23 July 2008 (UTC)

Acroterion, it's not much use having an administrator who openly admits that he doesn't understand the content of the dispute and who directs his complaints generally at everybody involved in the dispute. That is not how disputes are resolved.

Have you ever thought about enquiring into why this group are so determined to mask the truth regarding centrifugal force? You have seen for yourself how they denied that a marble on a rotating turntable would roll outwards along a radial groove. They denied that and deleted my edit on the matter as a result of which I got blocked for a month.

Do you not have the least curiosity to ask yourself why these people are denying such a basic fact?

You have now seen them attempting to deny the involvement of centrifugal force in planetary orbits despite the fact that I have supplied a very professional reference on the matter.

Are you not ineterested to know what is the driving force behind this corrupt behaviour coming from these young college students? I can tell you exactly what it is. These guys are uncomfortable with the fact that centrifugal force is an absolute effect. It contradicts the philosophy that they were introduced to at university that all things are only relative and that nothing is real.

That's what it's all about. It is a fanatical group of denilaists just like the other group over on the Mozart page who are in total denial of the fact that Mozart was a German despite a large number of citations which indicate the contrary.

These kind of people seem to gather together and dominate many of the pages on wikipedia. Are you one of that kind? David Tombe (talk) 01:31, 24 July 2008 (UTC)

The chief subject of my curiosity is your lack of irony as you report that you've stirred up another article, and that another conspiracy involving an entirely different set of editors has coalesced to oppress you. I call that a clue, not a conspiracy. Acroterion _(talk) 12:10, 24 July 2008 (UTC)

David, these kinds of remarks are the reason you've been blocked so many times. Some of the editors you call "young college students" are experienced physicists with PhD's, who have published in reputable mainstream journals. You could learn from them if you'd listen, instead of constantly arguing with them. Their interpretation of the sources is in line with the mainstream view as required by Wikipedia's WP:NPOV, WP:RS and WP:OR policies. They have been reverting your misinterpretation of sources, and have tried to explain the material to you. Personally, I gave up on trying to discuss this with you a long time ago. Plvekamp (talk) 02:08, 24 July 2008 (UTC)

Hey, plvekamp, that is just plain wrong. Mr Tombe is correct that the editors are biased, I have seen it. You guys just dont want to see yourselves as users see you. Users see you as biased ego tripping brutish thugs who delete edits of those you dont like. You are just an unfair biased clique who dont want to straighten out your mean and nasty behavior towards users who are not members of your clique. Administrators are as bad as the others. Wikipedia is just a poorly written stupid excuse for an encyclopedia. You need to reform it so it can really be something worth while, but you are too busy ego tripping. 72.64.54.150 (talk) 16:31, 24 July 2008 (UTC)

Potential energy section

I suggest replacing into the potential energy section the sentence: The Coriolis force has no equivalent potential, as it acts perpendicular to the velocity vector and hence rotates the direction of motion, but does not change the energy of a body. It was removed by DT because he claims it is controversial. It is not. He is the only one who thinks so. He has an original theory about potential energy of Coriolis and magnetic forces.

I shouldn't worry about it. It's self-evident that coriolis doesn't change the energy (since the speed of a particle is not changed by it), but I couldn't find a reference when I looked. Not everything that's true can go in the wikipedia, if it's not verifiable that's it true. C'est la vie.- (User) WolfKeeper (Talk) 16:10, 24 July 2008 (UTC)

I would also like to add something to the section about centrifugal and gravitational potential on the surface of the earth. Here's a stab:

Calculations done in the reference frame of the earth (or any other rotating planet) can be simplified by combining the centrifugal potential with the gravitational potential. The gradient of the resulting potential function is the effective gravity, and can be treated as a single force field. It does not matter, dynamically, how much of the force is due to gravity and how much to the centrifugal effect. The equipotential surfaces of the combined potential are everywhere perpendicular to the direction of effective gravity, which is the direction shown by a plumb-bob. Mean sea level is one these equipotential surfaces.

Rracecarr (talk) 14:41, 24 July 2008 (UTC)

Racecarr, I dont understand what you mean by this. Since the article is about an apparent force and not a real force this entire topic seems to be a lot of calculations regarding a force that doesnt really exist. You guys seem very confused to me. Is this article about a real force or an apparent, fictitious force or is it about something else? You need to get clear what you are talking about in this article.72.64.54.150 (talk) 16:42, 24 July 2008 (UTC)

Oh, no, it's perfectly real, it's just one facet of inertia.- (User) WolfKeeper (Talk) 17:17, 24 July 2008 (UTC)

RRacecarr, Coriolis force does indeed act at right angles to the motion. But so does centrifugal force. Hence that cannot be used as a reason for why Coriolis force doesn't have an associated potential energy.

Furthermore, on closer examination, it is clear that centrifugal potential energy is actually just tangential kinetic energy.

In an irrotational gravity field, we can substitute the Keplerian areal constant into the centrifugal potential energy term and obtain an inverse square law position dependent expression for centrifugal potential energy. It's all on page 77 of Goldstein's. The combined gravitational potential energy and centrifugal potential energy leads to a graph just like the inter-atomic forces potential energy graph. And it is a radial effect similar to what you said above regarding combining gravity and centrifugal force into one.

In an irrotational field, Coriolis force only changes the direction of an object and so there is no potential energy involved.

But the wording in the sentence that I removed, does not accurately refelect this state of affairs. I told you at the beginning that all the facts were correct but that the reasons weren't the reasons for the facts.

I should also add that in an irrotational field, I can't think of any way of obtaining a Coriolis force apart from externally applying one, such as in the example of water flowing radially through a pipe that is fixed on a rotating turntable.

To obtain a Coriolis force naturally we would need a vortex field such as we get in magnetism. In that case we could indeed have a Coriolis potential energy simply by considering the radial kinetic energy and a gradient taken on the basis of a tangential coordinate.

It's best that this topic is taken to the Coriolis force page since is is only cluttering up an article on centrifugal force that is already top heavy with irrelevencies. David Tombe (talk) 18:42, 24 July 2008 (UTC)

I don't intend to carry on a discussion of this matter, but: in a rotating frame, the centrifugal force always acts outward, regardless of the motion of the object. The object can be moving in any direction. In particular, it can move parallel to the centrifugal force, and when it does, the centrifugal force changes its energy. By contrast, the Coriolis force always acts perpendicular to the motion, and never changes the object's energy. Rracecarr (talk) 18:50, 24 July 2008 (UTC)

Rracecarr, you are obliged to carry on the discussion. The Coriolis force as you say does always act perpendicular to the direction of motion, just like the F = qvXB force in magnetism. You use the F = qvXB force in magnetism to account for the force acting between two magnets. And you know that magnetic repulsion has an associated potential energy.

So you must also know that Coriolis force has a potential energy in a vortex. You being a meteorologist know that you apply the Coriolis force in those large vortices called cyclones that can be viewed from space.

Hence, the Coriolis force cannot be fictitious, and it must have an associated potential energy. That is why I don't come to the Coriolis force page. It is beyond redemption. It couldn't possibly be corrected within wikipedia's rules and regulations.

But centrifugal force can be corrected. A formula of words can be devised which does not contradict the textbooks. David Tombe (talk) 19:22, 24 July 2008 (UTC)

I am not obliged to continue this discussion, and in fact I won't. You are confused--which is fine: I would enjoy helping you understand if you'd listen--but you are completely unwilling to learn, so the effort is pointless. I only have so long to live. I do not believe arguing with you is a good way to spend time. Rracecarr (talk) 19:29, 24 July 2008 (UTC)

This is the kind of topic that very intelligent people can have a lot of trouble with.- (User) WolfKeeper (Talk) 19:38, 24 July 2008 (UTC)

David, with all due respect I think that as long as you continue to fail to grok what a coordinate transformation is, and why it applies with total generality to all motions (not just limited circular or elliptical ones), and how the resulting equations and accelerations are completely in-line and equivalent to (indeed part of) Newtonian Mechanics then you will continue to contribute extremely poorly.- (User) WolfKeeper (Talk) 19:38, 24 July 2008 (UTC)

It seems to me that this is exactly what Mr Tombe has been saying. Now you are saying what Mr Tombe has said. But you blocked him for saying this. So it seems you are either mistaken or just plain prejudiced against Mr Tombe. So explain why you deleted his edits when he is saying just what you say here. I think you are just confusing things, and act out of disrespect towards Mr Tombe for no real reason that makes sense to me. I certainly can see why Mr Tombe is argry with you guys, you appear to be hypocrits.72.64.54.150 (talk) 18:58, 24 July 2008 (UTC)

We did it because of this cartoon.[1]- (User) WolfKeeper (Talk) 19:44, 24 July 2008 (UTC)

Thanks for the chuckle, Wolf. Kinda puts this waste of argument in a nutshell ! My sides hurt. Plvekamp (talk) 19:05, 26 July 2008 (UTC)

Isn't centrifugal force simple?

It always seemed to me that it was simply a matter of "prevented inertia". In other words, a ball on a string is being propelled in a straight line until the string pulls the ball off line and into the circular motion around the center.

In the instance of sitting in a car, the car turns a corner, my body wants to continue in a straight line, which it does until prevented by the door or my seatbelt, and my forward propulsion is curved off the line.

What is fictitious about that? dgaubin (talk) 16:46, 29 July 2008 (UTC)

Nothing. That's centripetal force, which is a real force. This article is basically about inertia, which isn't fictitious, but is associated with a pseudo force which acts outwards in non inertial frames of reference, such as the surface of the Earth.- (User) WolfKeeper (Talk) 17:13, 29 July 2008 (UTC)

It's a question of the language that we speak in. In X, Y, Z, it's inertia. In polar coordinates it's centrifugal force. The argument has been over whether centrifugal force is acting in a non-rotating bucket of water when it is viewed from a rotating frame of reference. When a bucket of water is really rotating, there really is a centrifugal force which causes the water to climb up the walls of the bucket. But what about a stationary bucket of water as viewed from a rotating frame of reference? The water doesn't climb up the walls of the bucket. I say that that means there is no centrifugal force. Most of the rest of the editors here say that there is a centrifugal force but that it has been over ridden by a radially inward Coriolis force that is twice as strong. David Tombe (talk) 19:27, 29 July 2008 (UTC)

No. At (X,Y,Z) in a rotating frame of reference it's the centrifugal pseudo force (Fx,Fy,Fz). This article is not about polar coordinates, strangely the polar coordinates article is about that; go ahead, and knock yourself out. Did I mention that you need to be at the polar coordinates article David? Because you should be over at the polar coordinates article. Get it? Polar... coordinates article. Centrifugal force is defined differently in polar coordinates, as is the coriolis force. The coriolis force is always transverse in polar and the centrifugal force depends only on the motion of the particle. In rotating frames of references it can be shown that the centrifugal force that appears is proportional only to distance from the rotation axis. The force equation is similar, but the 'w' that appears refers to a completely different quantity (in this article, it's the frame rotation, in the polar coordinates article it's the particle's angular motion about the origin. They are NOT the same, and do not mean the same thing.- (User) WolfKeeper (Talk) 20:23, 29 July 2008 (UTC)

No, David the coordinate system in use is irrelevant for the physics. Anything that there is to be said about centrifugal force, can in principle be said in coordinate independent terms. This is why I suggested you study GR. Not because we need GR, but because the language in which GR is phrased is very particular about using coordinate independent quantities. I would explain this too you, if I thought you would listen, but its very clear to me that you won't, so I won't bother.

Your lack of understanding if the intricacies of dealing with different coordinate systems is what keeps sending you off on wild goose chases. The main problem is that you fail to realize that generally in a coordinate system you cannot directly compare velocities at different points space. This in general requires the use of a connection. One of the special properties of Cartesian (XYZ) coordinates is that the connection (on flat space) happens to be trivial, allowing direct comparison of velocities at different positions and consequently simplifying the calculation of accelerations and forces. The connection for polar coordinates is however non-trivial, and thus introduces extra terms when calculating accelerations. (TimothyRias (talk) 12:48, 30 July 2008 (UTC))

It's good to avoid being dogmatic about these things, because it is, after all, just a matter of convention as to which terms arising from a non-trivial spacetime connection we choose to call "acceleration corrections" and which terms we choose to call "fictitious forces". As you said, we can learn lessons from relativity, and one of the main lessons is that physical phenomena are most naturally expressed in terms of a unified spacetime representation, rather than treating space and time on fundamentally different footings. From the spacetime point of view, there is just a single "connection", and any non-linearity of either the spatial or the temporal coordinate axes (relative to inertial worldlines) leads to correction terms. The question is what we choose to call these terms. (Of course, it doesn't really matter what we call them, but the inconsequentiality is what makes the topic so conducive to argumentation!) We could call them all corrections to our accelerations, or we could call them all fictitious-forces, or we could call some fictitious-forces and some acceleration corrections. It's really just a throwback to pre-relativistic thinking to treat the terms arising from spatially curved coordinates one way, and the terms arising from temporally curved coordinates a different way. (You can find a detailed discussion of this topic if you do a google search on "curved coordinates and fictitious forces".) It's a nice irony that Mr. Tombe, an anti-relativity zealot, was actually advocating the more sophisticated relativistic point of view here (although he didn't realize it and would probably deny it), whereas the other editors, who consider themselves to be supporters of relativity, have been doggedly defending the pre-relativistic conventions (although they don't realize it and would probably deny it). This is what makes Wikipedia so entertaining (a battle between the half-wits and the half-wise).63.24.38.196 (talk) 04:14, 2 August 2008 (UTC)

I doubt if you'll hear from Mr. Tombe till November. He has been blocked for three months. (Rheinhardt K. (talk) 00:12, 3 August 2008 (UTC))

What is a "scalar force"?

At the start of the current article there appears a list of pointers to other article, and the last item on the list says "For the scalar force that appears in polar coordinates, see the article on polar coordinates". I checked the article on polar coordinates, and the word "scalar" doesn't appear there. So, what exactly IS a "scalar force"? And why does the article point to another article for explanation of something that isn't even mentioned in the other article? Surely something is amiss.63.24.61.29 (talk) 20:48, 2 August 2008 (UTC)

Of course, you are correct in pointing out the absurdity of a "scalar" force. This pointer should be removed altogether, but I have only edited it to remove the absurdity. The history of this article shows that this pointer was a concession to a long, drawn out battle that apparently exhausted all parties and led to this compromise. Brews ohare (talk) 15:45, 3 August 2008 (UTC)

Any single dimension is a scalar- a scalar is simply a single number. There's nothing absurd about a scalar force any more than there is about a scalar acceleration. What is 9.81 m/s^2?- (User) WolfKeeper (Talk) 16:14, 3 August 2008 (UTC)

I don't understand the "corrected" version. The acceleration component that it refers to (i.e., the one that arises in stationary polar coordinates) is explicitly described and given the name "centrifugal force" in countless reputable references, including:

(1) "An Introduction to the Coriolis Force" By Henry M. Stommel, Dennis W. Moore, 1989 Columbia University Press.

(2) "Methods of Applied Mathematics" By Francis B. Hildebrand, 1992, Dover, p 156.

(3) "Statistical Mechanics" By Donald Allan McQuarrie, 2000, University Science Books.

(4) "Essential Mathematical Methods for Physicists" By Hans-Jurgen Weber, George Brown Arfken, Academic Press, 2004, p 843.

This has been pointed out previously, with the relevant quotations. I don't think there can be any dispute of the fact that this particular acceleration term is indeed among the terms that are called (in contemporary reputable sources) centrifugal force. Needless to say, it's entirely a matter of convention as to what names we give certain terms appearing in certain equations, but since Wikipedia articles are supposed to reflect verifiable facts from reputable sources, I can't see any justification for excluding this particular fact from the article. I think any discussion of the contemporary (let alone the historical) concept of centrifugal force is incomplete if it doesn't include this.

There are also other concepts that go under the name "centrifugal force" but that are not yet mentioned in this article. And conversely, there are lots of things discussed at length in this article that are only indirectly related to the concept of centrifugal force. I understand that much of this material has been added as part of a tutorial on general physics being given to placate some of the editors here, but ultimately I think it detracts from the readibility and relevance of the article.

Overall I think the present article has evolved into a lengthy set of notes that various people have made as they clarified in their own minds certain aspects and implications of the centrifugal force, as they responded to challenges from certain other editors. Sort of learning on the job. That's a commendable exercise, but it doesn't make for a very coherent article, and frankly, the "on the job learning" still has a long ways to go before it arrives at a fully consistent and complete account of centrifugal force. I'm not sure if this is really the best and most efficient way of authoring Wikipedia articles. (It may be... I'm really not sure.) If nothing else, I guess people are having fun.63.24.126.122 (talk) 16:34, 3 August 2008 (UTC)

The thing you're failing to understand is that fundamentally this is an encyclopedia, and encyclopedias have an article per definition, whereas a dictionary has an article/entry per word/phrase and has multiple definitions within that. So the wikipedia has to define a term and then describe it. We've decided that dividing the term up along these technical grounds is the way to go. Coordinate transformation centrifugal force goes in this article (sister article to coriolis effect), polar centrifugal force/effect is in the Polar coordinate system article, reactive centrifugal force is over there. Ultimately it is an editorial decision in conjunction with the various definitions that there are as to how the wikipedia is laid out, but this is the way it seems to be best to do it.- (User) WolfKeeper (Talk) 16:46, 3 August 2008 (UTC)

Scalar forces

I believe this pointer is better left out in the first place, or a separate discussion should be added in this article. The whole idea that the radial term in polar coordinates is a centrifugal force in any sense of the word is a stretch to begin with. Were it not for D Tombe, I doubt that this idea would ever surface. Brews ohare (talk) 16:39, 3 August 2008 (UTC)

Forget him, we need to do the right thing; we're narrowly swinging too far the other way, it deserves a link out- there is indeed a usage in polar coordinate systems, it's less common, and it's not the same thing. And because it's not the same thing, the description shouldn't be in this article, but we need to at least link it.- (User) WolfKeeper (Talk) 16:46, 3 August 2008 (UTC)

By calling it a "stretch" I agree with you that the polar coordinate thing is not a fictitious force in the sense of being related to a non-inertial frame of reference. Rather, it is a term that appears in even an inertial frame of reference when polar coordinates are used, and has been referred to in the literature (in a totally confusing way that brings with the confusion absolutely no advantages) as "centrifugal" only because of its formal similarity to the formula for centrifugal force. Brews ohare (talk) 16:54, 3 August 2008 (UTC)

Your point of view seems to be that terms arising from the use of curved temporal axes may be called fictitious forces, but terms arising from the use of curved spatial axes may not, or at least that the latter constitutes a sufficiently different meaning of the term "centrifugal force" that it doesn't belong in the same article. You're certainly entitled to that point of view, but I question whether you're entitled to impose it on this Wikipedia article, especially since it is contrary to multiple reputable contemporary sources.

At the risk of discussing the subject of the article (which we're not supposed to do on Discussion pages), just think for a minute about a particle moving around in a circle of radius r with constant angular speed w relative to a system of polar coordinates rotating with speed W. The radial equation of motion is r" = f + r(W+w)^2 where f is the centripetal force (per unit mass). The total absolute angular speed of the particle is W+w, and the "extra" term that appears in Newton's law is r(W+w)^2. We might choose to treat this acceleration term as if it was an outward force, balancing the inward-pointing force f. This is the whole concept of fictitious force. But your position is that the "true" centrifugal force consists only of rW^2, and the rest of the terms (2rWw and rw^2) you believe should be called something else. Essentially you are trying to impose the old pre-relativistic segregation between spatial and temporal components of spacetime coordinate systems, and there are certainly plenty of reputable texts that adopt the same pre-relativistic point of view (although most of them take this naive approach only because they don't think anyone cares, not because it's justified). Nevertheless, there are also many texts that take the more sophisticated relativistic point of view, and reject any segregation of spatial and temporal components as artificial and meaningless.

I guess the question is whether this Wikipedia article should recognize all of these reputable sourced views of the subject, or reject all but the naive pre-relativistic view (as you advocate). From my reading of Wikipedia policy, if there are multiple views of a subject to be found in a significant fraction of the reputable contemporary sources on that subject, then all of those views are to be represented in the article.63.24.99.40 (talk) 20:09, 3 August 2008 (UTC)

Only if they're within the scope of the article, at the moment the scope is Newtonian, and rotating reference frames, as with the Coriolis effect article.- (User) WolfKeeper (Talk) 20:18, 3 August 2008 (UTC)

If you want to create an article on relativistic centrifugal force, by all means go ahead.- (User) WolfKeeper (Talk) 20:18, 3 August 2008 (UTC)

There can be little doubt that fictitious forces are different from the so called centrifugal acceleration terms found in polar coordinates. Thus, whatever the history, utility and beauty of these last, they belong in this article only to say that they do not belong here. Brews ohare (talk) 21:04, 3 August 2008 (UTC)

Hmmm... I've presented a well-reasoned and well-sourced case for why the full meaning of the term centrifugal force in contemporary reputable sources ought to be included in the article, and even explaining in detail why those reputable sources say what they say, i.e., the rationale for regarding the fictitious forces arising from curved coordinates to be the same category of conceptual entity, regardless of whether the curved axes happen to be just the time axis or just the space axes or any combination of those. In response, you say "there can be little doubt" that I'm wrong. Well, based on the facts as I've described them, and on your inability (or unwillingness) to offer any subtantive rebuttal, I would say we can proceed to modify the article along the lines I've suggested, i.e., more in conformity with Wikipedia policy and less reflective of the personal POV of individual editors.

In answer to Wolfkeeper, the subject here isn't relativistic centrifugal force, it is centrifugal force as grasped by people who have learned the epistemological lessons of relativity (and the rest of modern science), even though these lessons haven't found their way into some introductory engineering texts. I would also point out that the present article claims to be based on relativity, and even quotes Einstein's first postulate, so I don't think you can rationally claim that the current article excludes what it regards as the relativistic view of the subject.

Well, I agree with this latter point, the article shouldn't include relativistic definitions and so I have removed it. This article is really a sister article to Coriolis effect and that doesn't discuss polar coordinate systems or relativistic mechanics either. I would encourage you to start an article on that particular, quite different topic, but on practical grounds, I don't see that this article can be stretched to include both.- (User) WolfKeeper (Talk) 21:38, 4 August 2008 (UTC)

Well, I think you two have given me a good indication of the level of discourse (and intellectual honesty) here, and I think I'm out of my league, so I'll bow out and leave you to it. Good luck.63.24.104.68 (talk) 21:34, 3 August 2008 (UTC)

I believe I have been responsive in describing exactly why the polar coordinate terms are not the same breed of cat as the fictitious forces. Your answers to this are not responsive. Instead, you drag in vague ideas like curved time axes, etc. without addressing specific items in the article, or replying to suggestions given. Brews ohare (talk) 21:47, 3 August 2008 (UTC)

Centrifugal force and polar coordinates

I'm going to support ip 63.34.xxx.xxx (btw, please register a user name it makes it easier to recognize your posts) on this. The term present in equations in polar coordinates and the term present in rotating reference frames are two sides of the same coin. (i.e. they are terms coming from the non-trivial connection coefficients involved in calculating the acceleration.) I think this article should cover both. Especially, since there is a whole bunch of textbooks that don't really distinguish between the two. (Marion and Thornton is one of them.) I do however see problems in providing a unified definition of the two, that distinguishes them from other fictious forces. (TimothyRias (talk) 16:47, 4 August 2008 (UTC))

They're not two sides of the same coin, because one centrifugal force is frame related (the force is proportional to the square of the rotation rate of the frame, and independent of the motion of the particle) whereas the polar coordinates is entirely object related (it depends on the rotation rate of the *object* around the origin). If you have a reference that says that they're the same thing, then we need that to make changes to the article, otherwise you're wasting our time. And quite frankly, that's the whole point, that they're not the same. Or, if all you're say is the trivial truth that the effect of centrifugal, coriolis etc. in both rotational frames of reference is the same as polar coordinates is the same as any other coordinate transformation that is equivalent to Newtonian Mechanics, then yeah, so? That doesn't mean that all coordinate transformations should be in this article, because the same argument applies to them also. And even that argument ignores the fact that this is a 3D vector treatment, whereas polar is only 2D.- (User) WolfKeeper (Talk) 20:19, 4 August 2008 (UTC)

I weigh in with Wolfkeeper on this: the mathematical terms in polar coordinates have not only no physical connection to fictitious forces, they also are completely unrelated mathematically to these forces except for the circular motion case, where you could argue that (when multiplied by a mass) they express terms that are the negative of the fictitious forces, but only in that limited case.

The reason for agreement in this singular case is that for circular motion the circle traversed happens to be the osculating circle for the entire path, and the center of polar coordinates happens to be the same as the center of the osculating circle. Remove either of these accidents and you lose any connection. I believe the distinction has been made very clearly and correctly in this article and in the polar coordinates article and again in the centripetal force article. Brews ohare (talk) 22:00, 4 August 2008 (UTC)

About polar coordinates being 2d, that's irrelevant the same term appears in 3d extensions of polar coordinates (i.e. spherical or cylindrical coordinates).(TimothyRias (talk) 08:13, 5 August 2008 (UTC))

I agree that dimensionality is irrelevant at a fundamental level. However, even in two dimensions a general planar motion does not lead to the polar coordinate expressions. You have to use the osculating circle. Have you thought about this point? It has come up earlier. See this. And this. Brews ohare (talk) 11:38, 5 August 2008 (UTC)

That is only necessary if you want the motion to be tangential at every point of the curve, and is an approach that I would not recommend. But there is no reason you couldn't describe an arbitrary planar curve in a single set of polar coordinates. (TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Hi Timothy: I'm left-adjusting the format of these comments so they are easy to find. The objective is not to describe a curve, but to describe a motion along a curve. Otherwise we are doing analytic geometry. not mechanics, and there is no "acceleration" and no "time dependence". If you track a motion, the kinematics of the motion must be referred to the osculating circle, a circle with time-shifting center in general, to determine the centripetal force in an inertial frame of reference. (See Curtis.) This centripetal force becomes the centrifugal force in the non-inertial frame of motion attached to the moving particle. See here. Brews ohare (talk) 15:34, 5 August 2008 (UTC)

About there being no physical connection I beg to differ. A change of frame is just a time dependent change of coordinates. That is it is just a change of coordinates in spacetime. (TimothyRias (talk) 08:13, 5 August 2008 (UTC))

There are many meanings of "frame". See Frame of reference, for example. However, here is the key issue: there are inertial frames and non-inertial frames. In inertial frames there are no fictitious forces That includes no centrifugal force. However, in an inertial frame you can use a time dependent coordinate system, like a polar coordinate system that tracks the particle. That does not mean you left your inertial frame. It means only that you adopted a time-dependent description of what you see from your viewpoint. Just like you can adopt a teen-ager's vocabulary to describe life, but that doesn't make you a teen-ager: you'll still be talking about pensions, retirement, and health care. On the other hand, you can jump onto a particle and share the particle's motion. Then you are in a non-inertial frame. The particle is at rest in this frame. However, if you want to explain various matters, you need to introduce fictitious forces, like centrifugal force. Otherwise, you don't understand why you are being pushed around even though you are at rest in your frame.Brews ohare (talk) 11:38, 5 August 2008 (UTC)

(Since when are polar coordinates time dependent?)(TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Hi Timothy: If you track motion, the motion is time dependent. And then the polar coordinates describing the motion are time dependent. (See here.) Brews ohare (talk) 15:34, 5 August 2008 (UTC)

Note that that is not what people usually mean with polar coordinates. (TimothyRias (talk) 08:39, 6 August 2008 (UTC))

Once you move into the general setting of (curved) spacetime the concept of a frame loses its (global) meaning. At best it has some local meaning. This because in a curved space the exponential map is not an isometry (as it is in flat minkoswki space.) The lesson from this is that viewpoints are inherently local. When comparing events at different points we must also account for the fact that we have to make a choice of "frame" at each point. If we have chosen coordinates, then this gives us an easy canonical way of choosing the local frame at each point, and thus of comparing events. In flat space choosing anything other than cartesian coordinates (with the usual SO(3,1) ambiquity) will lead to a non trivial comparison between points. Technically we will have non-zero connection coefficients. Going back to a 3d description by picking equal time slicings, will then give a description in which velocities and accelerations have picked up extra terms, which may or may not be interpretet as fictitious forces. From this point of view the centrifugal terms in rotating frames and polar coordinates arise exactly in the same manner. (TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Well said.130.76.32.15 (talk) 20:14, 5 August 2008 (UTC)

Hi Timothy: I have no ambition to discuss relativistic formulations. I'll bet Marion and Thornton don't do that either, in this context, eh? Brews ohare (talk) 15:34, 5 August 2008 (UTC)

For a more down to Earth connection. In a central force problem, integrating out the integral of motion connected to rotational invariance (i.e. conservation of angular momentum) leads to the same centrifugal term no matter what coordinates you started in.(TimothyRias (talk) 08:13, 5 August 2008 (UTC))

If you are talking about analyzing the problem in polar coordinates, you get the polar-coordinate expression for "centrifugal acceleration". If you did the problem in elliptical coordinates, or in arc-length coordinates you would not. If you are looking at angular momentum, a constant of the motion in the central force problem, it is coordinate system independent. But that is not the same discussion. If you want to call some contribution to the angular momentum in some particular problem a "centrifugal contribution" that is a confusing choice of terminology, but it is a different confusion than the discussion of the polar coordinate acceleration term. Brews ohare (talk) 11:38, 5 August 2008 (UTC)

I'd also love to see you guys give an explicit citation backing up your claim that there is absolutely no physical connection between the two. Otherwise I don't think the wikipedia article should be making such a strong claim. (TimothyRias (talk) 08:13, 5 August 2008 (UTC))

The discussion of inertial and non-inertial frames above explains why there is no physical connection. There are already citations in the articles that state clearly that centrifugal force is a fictitious force and does not appear in an inertial frame. The polar coordinate acceleration appears in all frames that employ polar coordinates, inertial or non-inertial. Brews ohare (talk) 12:01, 5 August 2008 (UTC)

That there isn't a connection in the scope of 'classical' classical mechanics (in which global frames have a meaning) does not mean that there is no physical connection, period. There are many examples where a more general theory is necesary to explain the connection between different seemingly different concepts. This is one of them. (TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Hi Timothy: Well, in the big picture, maybe everything is connected. But within the framework of this corner of mechanics, with the usual definition of inertial frames (Lorentz or Galilean related), there is no basic connection; only an accidental connection in the case of circular motion. (The source of this accident already was described here.) Brews ohare (talk) 15:34, 5 August 2008 (UTC)

It is probably better to just mention the clear fact that both are referred as centrifugal force.(TimothyRias (talk) 08:13, 5 August 2008 (UTC))

The fact that the same name is used for both is already in the articles, and the differences are also pointed out. Brews ohare (talk) 11:38, 5 August 2008 (UTC)

But the better argument may be that there is plethora of textbooks out there that treat them as the same.Mostly without actually explaining the deeper connection between the two. (An example of this is the Marion and Thornton book (again since it is the one that's on my desk) in the chapter on central forces it mentions that the term appearing in the (polar coordinate) formula is called the centrifugal force, but that it is not a force in the usual sense and then defers to the section about fictitious forces for a more detailed treatment.) (TimothyRias (talk) 08:13, 5 August 2008 (UTC))

To treat them as the same is a shocker. However, the context of the central force problem may be the cause of confusion. It may be that in this problem a number of different items are accidentally similar. A more general case would show up differences. The "not a force in the usual sense" phrase sounds like a ducking of clear thought. I do not have access to this text. Can you find a comparable discussion that is available in some detail on googlebooks?? Brews ohare (talk) 11:38, 5 August 2008 (UTC)

I can have a look. (TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Here are a couple of references accessible online:

"An Introduction to the Coriolis Force" By Henry M. Stommel, Dennis W. Moore, 1989 Columbia University Press. "In this chapter we have faced the fact that there is something of a crisis in intuition that arises from the introduction of the polar coordinate system, even in a non-rotating system or reference frame. When we first use rectilinear coordinates to understand the dynamics of a particle, we commit our minds to the simple expressions x" = F_x, y" = F_y. We think of the accelerations as time rate-of change [per unit mass] of the linear momentum X' and y'. Then we express the same situation in polar coordinates that partly restore the wanted form. In the case of the radial component of the acceleration we move the r(theta')^2 term to the right hand side and call it a "centrifugal force."

"Statistical Mechanics" By Donald Allan McQuarrie, 2000, University Science Books. "Since the force here is radial, it is convenient to use polar coordinates. Taking x = r cos(theta) and y = r sin(theta) [i.e., stationary polar coordinates] then... If we interpret the term [r(theta')^2] as a force, this is the well-known centrifugal force..."Fugal (talk) 04:32, 6 August 2008 (UTC)

This means that a great many users (even those with physics degrees) reading this article are gonna assume they are (more or less) the same thing. Hence it should be discussed in the article. I don't think this would have to be a very lengthy discussion. The current not (with some further tweaking/sourcing) should probably suffice. (TimothyRias (talk) 08:13, 5 August 2008 (UTC))

I can see that readers of Marion and Thornton could get the wrong idea: after all, I think you did. I don't see how the reader of the Wiki articles could get the wrong idea, however. I hope that you haven't. You do appear to see that there is a different view on Wiki, anyway, but just don't see why. I'd like to see the articles written so that you would see exactly what is going on. So before you lose your initial perception of the articles, please make a note of what could be done to lead a reader by the hand. Brews ohare (talk) 11:38, 5 August 2008 (UTC)

Coming from a more general perspective, I think I've a clearer idea of what's going on than you. So, I'd appreciate a little less condecending tone. As for some suggestions on where to improve the article I'll come back to that later. (TimothyRias (talk) 14:40, 5 August 2008 (UTC))

Hi Timothy: Sorry for the appearance of condescension. I am just trying to explain things from a certain (apparently limited) viewpoint. However, this narrow perspective is the one commonly adopted for this topic. Brews ohare (talk) 15:34, 5 August 2008 (UTC)

The narrow perspective is probably OK for the article. However there appears to be a non negligible number of prominent sources that take an other perspective, hence the wikipedia article should at least mention it. And when mentioning it, it should probably refrain from making over the top strong statements such that there is no physical connection. A little bit of weaseling tends to be in order when the perspective of an article is limited. (TimothyRias (talk) 08:45, 6 August 2008 (UTC))

Fictitious vs polar centrifugal forces (Cont'd)

I am assuming that you are not referring to "weaseling" based upon "slices of space-time"? If that is what you mean, then please provide a reference (preferably one that can be read on googlebooks), and a quotation, and a summary of the issues. If instead, what you mean goes back to the confused state of terminology, that subject already has been adequately dealt with in Aside on polar coordinates, short of some inadvisable rant about authors that use a terminology in their topics on use of polar coordinates that is incompatible with their use of the identical terminology for fictitious forces in other sections of their very same book. Brews ohare (talk) 13:58, 6 August 2008 (UTC)

The terminology is incompatible (or rather, seems incompatible) only to readers who insist on imposing a pre-conceived but incomplete notion as to the meaning of "fictitious forces". The confusion is due mainly to the fact that authors of introductory texts sometimes split up the topic of fictitious forces into two parts, thinking that this will make it easier for students to understand if they present the consequences of curved space coordinate axes separately from the consequences of curved time coordinate axes. But unfortunately this pedagogical tactic tends to leave some students with a bifurcated view of what is really just a single concept. There is nothing more (or less) "physical" about the fictitious forces that arise in either case. Both are artifacts of using coordinate systems in terms of which the net applied force (per unit mass) does not equal the second derivative of the space coordinates with respect to the time coordinate. In both cases this coordinate effect can be corrected by the inclusion of additional acceleration terms (recognizing that the true absolute acceleration does not equal the second derivative of the space coordinates with respect to the time coordinate in these systems), or alternatively those extra terms can be negated and brought over to the other side of the equations and treated as if they were forces, hence fictitious forces. Some texts make the unity of this subject explicitly clear, whereas others obscure it, and still others present only the effect of curved time axes and never address the corresponding effect of curved space axes at all. Since Wikipedia articles are supposed to reflect the views published in reputable sources, I think the article should describe both the obscure disjointed view (which you advocate) and the clear unified view. It would be nice if the article could just be written giving the clear unified view, but since so many published texts present the outmoded and obscure view, I conceed that it needs to be represented as well. It may actually be useful, since it may help people avoid confusion.Fugal (talk) 15:18, 6 August 2008 (UTC)

Hi Fugal: In contrast to your viewpoint, I believe the article to provide a correct, well balanced and thoroughly documented viewpoint. That is, that there are multiple uses for the terms, and the one appropriate here applies to fictitious forces. It does not say that other uses are forbidden or "wrong", but that they are different. It does no good to lump them all together, when there are real physical differences between them. The most simple difference is that fictitious forces appear only in non-inertial frames of reference. Would you dispute this point? Consequently, the fictitious centrifugal force is different from the "polar coordinate" centrifugal term, which last appears in all frames, inertial and non-inertial. I find it difficult to debate this point; it is very well documented by the citations in the article. Brews ohare (talk) 04:32, 7 August 2008 (UTC)

Whenever acceleration terms appearing in the equations of motion due to non-linear coordinates are brought over to the other side of the equation and treated as forces, they are called fictitious forces (also known as inertial forces, pseudo forces, etc). This encompasses both accelerating coordinate systems and spatially curved coordinate systems, es explained in the numerous references that have been cited. Consider an isolated particle, free of any external forces (F=0), so it is following an inertial path, and suppose its motion is described in terms of a coordinate system x1,x2,x3,t. In terms of these coordinates we find that the second derivative of the space coordinates with respect to the time coordinate is not zero. In other words, the equation F = m d^xj/dt^2 = 0 is not satisfied. Nevertheless, we know the particle is following an inertial path, because no external forces are being applied, i.e., we know F = 0. One way of explaining this is to say that, in terms of our chosen coordinates, the absolute acceleration of the particle must not equal the second derivative of the space coordinates with respect to the time coordinate. There must be some other terms in the expression for the true absolute acceleration, and these terms must sum to zero. Alternatively we could choose to maintain the (sometimes convenient) fiction that the absolute acceleration equals d^2xj/dt^2 and we can still apply Newton’s law by bringing the extra acceleration terms over to the other side of the equation and pretending they are forces. Thus, as it says in Goodman and Warner’s “Dynamics”, the simple law F = m d^xj/dt^2 can be applied in terms of any system of coordinates, provided we include in F the sum of all fictitious forces, i.e., all acceleration terms (multiplied by mass) representing the difference between the true absolute acceleration and the vector d^xj/dt^2. Thus, fictitious forces arise in any non-linear coordinate system (i.e., any system in which the absolute acceleration does not equal the second time derivative of the space coordinates), and they arise in exactly the same manner, regardless of whether the non-linearity is of the time coordinate or the space coordinates or both.

It would be nice if you were able to understand this, but frankly, whether you understand it or not, the fact remains that this is how fictitious forces are comprehensively defined, as substantiated in the numerous references that have been provided, so there is simply no justification within the rules of Wikipedia editing for mis-representing these facts in the article.Fugal (talk) 15:05, 7 August 2008 (UTC)

Of course, in doing any mathematical manipulations, "convenient fictions" (your characterization above) may be introduced that suit the investigator's temporary conceits. However, the "fictitious" forces so introduced are not on a par with the much more fundamental issues that relate to the state of motion of the observer, that separate inertial from non-inertial frames, and that are not to be categorized as mere mathematical manipulations.

The choice of coordinate systems doesn't have any effect on actual physical phenomena. Fictitious forces are, by definition, artifacts of a particular choice of coordinate systems. They are all "mere mathematical manipulations". Also, the acceleration terms appearing with certain coordinates do not depend on the presence or state of motion of any observer. An accelerating observer can use inertial coordinates, and an inertially moving obvserver can use accelerating coordinates, and they can both use rectilinear or curved spatial coordinates. The choice of coordinate systems is arbitrary, and even with a given choice of coordinate systems, the choice of whether and which acceleration terms to bring over to the "force side" of the equation and treat as if they were forces is also arbitrary.Fugal (talk) 18:14, 7 August 2008 (UTC)

I don't think you understand fully the difference between a "coordinate system" (a mathematical concept) and a "state of motion" (a physical reality). It is a perversion of concept to suggest there is no difference between inertial and non-inertial observers. I find that virtually all texts on mechanics make a distinction. And fictitious forces appear only for non-inertial observers. See Frame of reference, Fictitious force and Inertial frame of reference for more detail on this. Brews ohare (talk) 22:31, 7 August 2008 (UTC)

It is you who plainly does not understand the difference between coordinate systems and states of motion. I can't comment on your "perversion of concept" statement, because it bears no relation to anything I've said. Likewise your follow-up statement that all texts distinguish between inertial and non-inertial is not pertinent to anything at issue here. Then you repeat your (thoroughly falsified) mantra that fictitious forces appear only for non-inertial observers. This is self-evidently false, and numerous references have been provided to you. You've read one of them, because you quoted it, when it specifically notes that coordinate systems in terms of which fictitious forces arise are not necessarily rotating. But by some truly bizarre psychiatric phenomena you've apparently convinced yourself that the book said just the opposite of what it actually says, so you continue to repeat your false claim. Weird.

And then to make this even better, you refer me to three Wikipedia articles for enlightenment, and a quick survery of the history of those pages shows that each of them was authored by (wait for it) Brews ohare! The fact that you're proliferating your fundamental misconceptions through multiple Wikipedia articles doesn't make you a reliable source. (See Wikipedia policies.)

Look, I've taken the trouble to provide you with SEVEN reputable published references from academic publishers, and all you've done is pointed me to three Wikipedia articles authored by yourself. Fugal (talk) 00:42, 8 August 2008 (UTC)

I don't appreciate your view of my limited abilities for understanding and your lofty validation of your own unsupported opinion. You might try less rhetoric and more communication. The views I have expressed are well-documented. Please, read the Wiki articles and the supporting citations. Brews ohare (talk) 16:22, 7 August 2008 (UTC)

The comments I've made here have not been "unsupported opinions", they have been accompanied with (so far) SIX different reference texts, all of which explicitly include the fictitious forces arising from curvilinear space coordinates. My comments have been honest attempts to convey the idea presented in those references. Undoubtedly it could be expressed better, but I'm doing my best. Having said that, I'm not sure what non-communicative "rhetoric" you are referring to.Fugal (talk) 18:14, 7 August 2008 (UTC)

Please provide me with links to these SIX supporting texts. Brews ohare (talk) 22:03, 7 August 2008 (UTC)

Links? Try reading a book from time to time. Here are the six references sources that have been provided to you (FOUR times now, so I hope you understand why I'm getting a little testy with you for insisting that you be spoon-fed repeatedly), plus a seventh for good measure:

(1) "An Introduction to the Coriolis Force" By Henry M. Stommel, Dennis W. Moore, 1989 Columbia University Press.

(2) "Methods of Applied Mathematics" By Francis B. Hildebrand, 1992, Dover, p 156.

(3) "Statistical Mechanics" By Donald Allan McQuarrie, 2000, University Science Books.

(4) "Essential Mathematical Methods for Physicists" By Hans-Jurgen Weber, George Brown Arfken, Academic Press, 2004, p 843.

(5) Marion and Thornton [ref by Tim Rais, "the term appearing in the (polar coordinate) formula is called the centrifugal force"]

(6) "Dynamics", Goodman and Warner, Wadsworth Publishing, 1965.

(7) "Statics and Dynamics", Beer and Johnston, McGraw-Hill, 2nd ed., p 485, 1972. —Preceding unsigned comment added by Fugal (talk • contribs) 00:25, 8 August 2008 (UTC)

I have reviewed the sources that I could access from your list. Those I looked at fall into two groups:

1. Authors whose main interest is polar coordinates and introduce the centrifugal force as "not real" and therefore "fictitious" in the sense of a mathematical convenience. These authors really are not interested in "fictitious forces" in the sense of classical mechanics, that is, in the relation to inertial and non-inertial states of motion. One cannot deny these authors their choice of terminology, but of course it is a different use of the term fictitious. Their point of view has been summarized in the present article and presented more fully in the article on polar coordinates.
2. Authors who do consider both the polar coordinate and the "state of motion" uses of the term. An example is Stommel and Moore, quoted at length earlier in these remarks. These authors use the term non-Newtonian instead of non-inertial to describe a rotating frame of reference, and repeatedly stress that rotation is different from simple use of polar coordinates in an inertial reference frame. This difference is exactly the distinction made in the present article.

So, I see no conflict with these references. Brews ohare (talk) 14:34, 8 August 2008 (UTC)

Fugal's sources

Stommel and Moore p. 4 "Sometimes the additional terms in the accelerations are transposed to the right side of the equation, leaving only the double-dotted terms on the left. So the acceleration terms on the right look like forces. They even acquire names such as "centrifugal force." As convenient as this may be from an intuitive, practical point of view, this transposition...can lead to confusion. ...So remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system. p. 26: "you should be very clear in your mind not to confuse the idea of a plane polar coordinate system fixed in inertial space with the idea of rotation of coordinates. This chapter is entirely tied to one particular reference frame, fixed in inertial space – so don't get mixed up now, or later when we introduce rotating axes." p. 36: This immediately gives the components of acceleration in polar coordinates, [lists equations] Remember once again that all this has nothing to do with rotating coordinate systems. We are in a polar coordinate system that is at rest with respect to the stars....The term r ω² then looks like a force, and it actually has a name: "the centrifugal force". ... But it is really not a force at all, and so if we want to make use of it in a formal sense, then we could call it a virtual, fake, adventitious force." Following these various cautions, these authors later proceed to a rotating frame (p. 54) where they again introduce polar coordinates, these now are polar coordinates in a rotating frame, and derive what is now the true fictitious force by analogy with the formulas for the polar coordinates in a stationary frame. They rely upon their earlier cautions about confusion, but (in my view) have done things in the way most likely to actually cause confusion. Nonetheless, they are perfectly clear that the two cases are different, and that they are exploiting a mathematical analogy.

I was unable to access the second source: "Statistical Mechanics" By Donald Allan McQuarrie. Brews ohare (talk) 17:13, 7 August 2008 (UTC)

As a correction, the Stommel and Moore reference was not mine, it was provided by Tim (Actually, it wasn't mine either, but the noname ip 63.something. (TimothyRias (talk) 12:02, 8 August 2008 (UTC))). Having said that, it's a fine reference, explicitly refuting your claims and confirming mine. By the way, I enjoyed your statement that when they discuss rotating coordinates they "derive what is now the true fictitious force", presumably as opposed to the false fictitious force that they derived for curved spatial coordinates, and had the nerve to call "centrifugal force". Let me just conclude this comment by repeating from your quotation: "So remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system."Fugal (talk) 18:37, 7 August 2008 (UTC)

Apparently we don't interpret these remarks the same way. Brews ohare (talk) 22:05, 7 August 2008 (UTC)

How about this... since you claim that Stommel and Moore support your position, I assume you have no objections to replacing your "Comment on Polar Coordinates" in the article with a direct repetition of the very words from Stommel and Moore you quoted above. Since you believe that the words "fictitious forces only appear in rotating frames" mean the same thing as "Remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system", you should have no objection to this substitution. And for everyone else in the world it reverses the meaning from being false to being true. So it's a win-win situation.Fugal (talk) 00:54, 8 August 2008 (UTC)

I personally make no such claim that fictitious forces only appear in rotating frames- clearly they appear in linearly accelerating frames and polar coordinates as well. The question is what the scope of this article should be. It has been agreed that it should be the radial force that appears in rotating frames, and in that way it forms the sister article to Coriolis effect. We have another article for polar coordinates. I also have no problem with including rotating polar coordinates here either. The question of scope is the most fundamental one, and this is not being addressed in the above discussion- and no reference to books can answer that- it is an editorial decision we have and must continue to make sensibly. I simply don't consider adding the 'centrifugal force' from fixed polar coordinates to be apropos in this article.- (User) WolfKeeper (Talk) 01:01, 8 August 2008 (UTC)

It might be helpful for you to review Wikipedia policies. When you say the decision of what to put in this article on "centrifugal forces" can't be answered by references to books (or presumably to any other verifiable sources), and instead should be determined by the personal "editorial decisions" of editors such as yourself, you are proposing a flagrant violation of Wikipedia policy. The article on subject X is supposed to accurately and faithfully represent the verifiable information about X to be found in reputable published sources. This is the cornerstone of Wikipedia. You're really not at liberty to impose your personal preference for the article to present only a partial and distorted version of what appears in reputable sources for this subject. The suggestion has been made that those editors who are fixated (for some unknown reason) on one particular aspect of the subject (such as fictitious centrifugal forces in rotating coordinate systems on Wednesdays and Saturdays, because by God there IS a clear distinction between the days of the week, and we've agreed to only consider Wednesdays and Saturday's in this article), then those people can start their own article on the subject "Fictitious Centrifugal Forces in Rotating Coordinate Systems on Wednesdays and Saturdays". I personally think that would be somewhat silly, but I certainly have no objection if you wish to do so. However, the article on centrifugal force needs to accurately represent the verifiable information to be found on this subject in the reputable literature. That is the Wikipedia rule. I trust no one here is advocating violating this basic Wikipedia principle.Fugal (talk) 06:10, 8 August 2008 (UTC)

There is no policy debate here. The article is about centrifugal force as treated in classical mechanics, and as it appears in common English usage (as in the centrifuge). The alternative (uncommon in everyday usage) use of the term as a catch-all for mathematical convenience in polar coordinates is properly outlined and referred to the appropriate article polar coordinates. The standard usage of "centrifugal force" as a fictitious force that appears in rotating reference frames is extremely well documented in the article using primary sources. Wiki policies have been scrupulously observed. Brews ohare (talk) 14:41, 8 August 2008 (UTC)

Fugal, you're right that I don't get decide alone. Ultimately it comes down to editoral consensus about what is normally meant by the term 'centrifugal force'- and whatever that is, it needs to be at centrifugal force in the same way that coriolis effect is what is meant there. I really don't think that centifugal force is just any force acting outwards, and I don't think that coriolis effect in polar coordinates is what is meant at coriolis effect.- (User) WolfKeeper (Talk) 03:26, 9 August 2008 (UTC)

While you're trying to understand the subtle nuances Fugal of the wikipedias policies you might like to try being less tendentious and offensive, and actually start to assume good faith.- (User) WolfKeeper (Talk) 03:26, 9 August 2008 (UTC)

Wolfkeeper. I suggest that you do the same for others. It has been a wikipedia policy to assume bad faith regarding everything that David Tombe does. Here you are acting in the same manner by berating Fugal. I thing that is a bit of a contradiction.72.64.63.178 (talk) 13:40, 9 August 2008 (UTC)

The difference is that Fugal understands thoroughly what the core of this topic is and is constructively discussing different ways to present the material, whereas David Tombe showed no signs at all of understanding at any point, and this lead him to waste considerable amounts of both his and other editors time.- (User) WolfKeeper (Talk) 14:00, 9 August 2008 (UTC)

Surely you are joking MR Wolfkeper. I didnt think humor was allowed. Maybe you are simply being dishonest in order to prove that what I said previously is true. You do treat Mr Tombe with disrespect. In any event, I cant see nothing wrong in repeating what has been said by Mr Tombe, concerning which you now seem to be agreeing with Fugal, when he says basically the same thing. "Citations are being ignored when it suits certain editors".

<duplicate of suspended user screed deleted>- (User) WolfKeeper (Talk) 15:39, 10 August 2008 (UTC)

It seems to me that Mr Tombe has been right all along and you simply just ignored and opposed his correct viewpoint, which now you seem to be agreeing with, since it is being advocated by a different editor. I certainly would like to know if you are now agreeing with Fugal and conceeding that he is right so that we can continue to complete this article?71.251.182.49 (talk) 12:27, 10 August 2008 (UTC)

You appear not to be assuming good faith. David Tombe paid lip-service to rotating reference frames, but was unable to explain why coriolis force is a vector quantity that can point in any direction perpendicular to the axis. This is inconsistent with the usage in weather systems, where the center of a cyclone or anticyclone is not aligned with the axis of the Earth. This shows pretty clearly that he didn't really get it, even if he says he did, even if you claim he did. They are similar, but *not* the same.- (User) WolfKeeper (Talk) 15:39, 10 August 2008 (UTC)

Sir, here you are attacking Mr Tombe, and that is not the point of this discussion. But if you seek to prove my point, I thank you for it. You have done so. You deliberately assume bad faith on the part of Mr Tombe, and so you have harassed him and unfairly blocked him and smeared his reputation. You continue to do that here by dead horse beating Mr Tombe who is unable to reply to your slanders. I think it is you who is being dishonest. You should frankly admit you have been wrong in this debate, and that Mr Tome and Frugal are correct in what they have said here. You and your supporters can then withdraw and let the article be completed without your blocking its progress towards completion.72.64.46.35 (talk) 20:55, 10 August 2008 (UTC)

Scalars and Vectors

On the subject of scalar forces. Please note that "scalar" does not simply mean single dimensional. It also implies being invariant under coordinate transformations. (A scalar is a rank 0 tensor, just as a vector is a rank 1 tensor) (TimothyRias (talk) 16:47, 4 August 2008 (UTC))

Well, it's invariant under rotation, who cares about translation in polar coordinates? And note that there's more than one definition of scalar anyway.- (User) WolfKeeper (Talk) 20:19, 4 August 2008 (UTC)

I weigh in with Timothy on this. "Who cares" is not an answer here. A vector has transformation laws under (for example) rotations, and just because you have a situation that does not explore this fact does not change the fact. Brews ohare (talk) 22:00, 4 August 2008 (UTC)

Centrifugal effect

Centrifugal effect redirects here. It's not a psychological effect (they're offtopic here anyway), it's an apparent acceleration in rotating reference frames, in the same way that coriolis effect is.- (User) WolfKeeper (Talk) 18:34, 3 August 2008 (UTC)

Actually, common usage is vague. In the case of Coriolis effect, it is very commonly used to mean Coriolis effect (perception). That refers to a lot of medical stuff about disorientation and nausea. Brews ohare (talk) 21:01, 3 August 2008 (UTC)

That's not the most common usage. The most common usage is in things like weather systems.- (User) WolfKeeper (Talk) 03:29, 9 August 2008 (UTC)

Suggested move/refactor to Fictitious forces in rotating frames

A radical suggestion: I propose that this article be moved to Fictitious forces in rotating frames, and that Coriolis force and Euler force be merged into it at the same time.

Rationale: the three "rotational" fictitious forces are all generated by the same physical phenomenon, and drop out as individual terms when the frame-transformation equation is differentiated and expanded. A detailed treatment of centrifugal force must necessarily include both of the others, and vice versa, and as a result both the Coriolis and Euler forces are already dealt with in this article.

After the merge we would thus end up with a single long fully-integrated article instead of one long article and two short ones with overlapping topics. Refactoring and copyediting work could then be more effectively applied to that single article, which I believe can be significantly shortened if a more general treatment is used, without treating centrifugal force as a special case that is separable from the other force terms.

At the same time, there are other related phenomena such as centripetal force and reactive centrifugal force and certain "centrifugal" terms in coordinate transformations which are not fictitious forces and not related to rotating frames, but are often confused with the rotational fictitious forces. Renaming this article will also make clear that the only topic being discussed is that of fictitious forces in rotating frames -- The Anome (talk) 12:11, 5 August 2008 (UTC)

You have stated the plusses of merger. However, one downside is that the combined article would be very, very long. That presents some questions of organization: it is tougher to make a clear, long article. Another downside is that "centrifugal force" is a magnet for dissension, and the other topics don't seem to attract so much attention. These debates might prove even more intractable in a longer article where they could spread like a grass fire. Finally, the reader who wants to find out about the individual topics will have to wade through a long, long table of contents to find what they want. My vote would be to leave things alone. Brews ohare (talk) 12:35, 5 August 2008 (UTC)

As Brews says, size is the big issue and there already is the article Fictitious force anyway.- (User) WolfKeeper (Talk) 15:43, 5 August 2008 (UTC)

I think it is a good very good idea. As I said before [2]: It is much easier to discuss centrifugal and Coriolis forces together than one at a time, since you rarely have one without the other. However, the existing articles should be kept and reduced to a more condensed and precise form. This would also give more room in the "centrifugal force" article for discussions about the etymology and historical perspective, and different uses of the term. The "fictitious force" article should only briefly state the results for rotating frames, and link to the new article for details. --PeR (talk) 20:37, 5 August 2008 (UTC)

I think it's a good suggestion. It would allow those who wish to restrict their attention just to the fictitious forces arising from the use of rotating coordinates to do so in the article devoted to that limited subject, while allowing the more encompassing meaning of "centrifugal force" as found in the literature to be fully represented in this article. I also agree with PeR that the existing article should be made more concise. (It has become nearly unreadable.)Fugal (talk) 04:24, 6 August 2008 (UTC)

I believe that the reason the article is so large is that it was expanded greatly during the recent phase of adversarial editing, to include a large number of worked examples. Many of these are very good, but they overlap one another, proving the same points over and over again in different ways. I believe that the article could easily be cut down to perhaps half of its current length by reducing the number of detailed worked examples, whilst retaining sufficient clarity and rigor of exposition. -- The Anome (talk) 08:20, 6 August 2008 (UTC)

User history indicates that you The Anome were actively editing during the adversarial phase in question. Did you make any attempt to control the adversarial expansion of the article? 86.141.250.16 (talk) 19:45, 10 August 2008 (UTC)

Even if so, I don't think it would be small enough to do much merging. And I completely disagree with the idea of re-merging reactive centrifugal force back here; the amount of usage of that concept is fairly low in the modern world, it gives it undue weight; and anyway it is logically quite distinct, under the wikipedias and general encyclopaedic rules it should not be merged here.- (User) WolfKeeper (Talk) 21:43, 6 August 2008 (UTC)

PeR- wikipedia articles are not about a term, they are about a topic or a concept. That's why reactive centrifugal force is not here- it's completely different, sharing only direction and having something to do with rotation.- (User) WolfKeeper (Talk) 21:48, 6 August 2008 (UTC)

The topic or concept in this case would be "force directed away from the center of rotation". It is not uncommon for Wikipedia to have articles on broad topics, optionally linking to more detailed articles on more specific sub-topics. The section on "reactive centrifugal force" would of course be relatively small, in order to avoid undue weight, and the longer discussion can stay in its own article.

The current state of the article will result in a steady influx of editors who want "their" definition of "centrifugal force" to appear in the article. Defending it vigorously against such edits will be counterproductive at best, and at worst scare new editors away from Wikipedia. --PeR (talk) 07:09, 8 August 2008 (UTC)

The notion of making the article noncontroversial is an interesting one. As a strategy, it would seem that what this means is that any article where debate may recur should be structured as a many-part article, with a part devoted to each perspective. That approach makes sense in some cases. Or, should we have centrifugal force (mechanics) and centrifugal force (polar coordinates)? I'd love to write the disambiguation page: For those of mathematical bent who do not see any difference between inertial and non-inertial frames, see centrifugal force (screwballs). To be more serious, it might be advantageous to have two pages for centrifugal force. My guess is that only the contributors to the present centrifugal effect page are really interested in the subject; the rest are interested in debate. So a narrowing (not broadening) of the subject will eliminate the phony dispute, or at least direct it to an insignificant minor topic page where it can go on and on and on and … who cares? Brews ohare (talk) 15:10, 8 August 2008 (UTC)

Well, centrifugal force (screwballs) would be a WP:POV FORK, and therefore, unfortunately, not allowed. The centrifugal force (polar coordinates) article doesn't need to be started until the section on polar coordinates becomes too large for the main article, and I don't think that's likely to happen. --PeR (talk) 18:25, 8 August 2008 (UTC)

Since wiktionary has 3 different definitions for the term, I've created centrifugal force (disambiguation).- (User) WolfKeeper (Talk) 03:47, 9 August 2008 (UTC)

This may be a good step toward straightening things out. Thanks. Brews ohare (talk) 04:15, 9 August 2008 (UTC)

Division of centrifugal effect into multiple pages

As a measure to limit useless debate over the proper content of the present page, I propose that the present centrifugal force page be renamed centrifugal force (classical mechanics) and new pages be started centrifugal force (general relativity), centrifugal force (polar coordinates) that are referred to by a disambiguation page: For the commonly used term centrifugal force and for the term as used in classical mechanics, see centrifugal force (classical mechanics). For the term as used as a mathematical convenience in polar coordinates, see centrifugal force (polar coordinates). For a very general approach useful to those with a background in general relativity see centrifugal force (general relativity).

Personally, I expect the other pages to develop very slowly as the main debaters on these issues have no real interest in contributing pages, and probably cannot bring enough muscle to bear to write these pages themselves. Brews ohare (talk) 15:27, 8 August 2008 (UTC)

This debate here has entirely been over centrifugal force in classical mechanics, so your suggestion doesn't really address the issue. (Also, your repeated reference to "polar coordinates" indicates that you don't have a clear understanding of what the issue.) All of the references that have been provided to you are concerned solely with classical mechanics. Of course, references don't do much good for people who can read a sentence like "Remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system" and interpret it as confirmation of their belief that such unreal forces appear only in rotating coordinate systems. I'm honestly not sure how to deal with such people, if we can't even agree on what a simple English sentence means. I think the only viable approach is what I outlined previously, i.e., we have to take the quotations you claim to agree with (like the statement that "the appearance of this type of unreal force does not necessarily involve a rotating coordinate system") and include them in the article verbatim. Then you can interpret them as confirming your beliefs, and all other readers can get an accurate and complete explanation of the subject.Fugal (talk) 16:02, 8 August 2008 (UTC)

Well, of course, that is an incorrect view of the situation. Within classical mechanics, the whole polar coordinate thing has at best a very subsidiary and limited role as a mathematical device, and no physical importance at all. As witness to the unimportance of polar coordinates, none of the examples presented depend upon polar coordinates, and a formulation entirely in terms of vector notation emphasizes the physics, again with no need for polar coordinates. Inasmuch as polar coordinates are such a source of confusion, it would be a relief to remove them entirely from consideration in this article and put that remote, derivative subtopic elsewhere. Brews ohare (talk) 23:38, 8 August 2008 (UTC)

No need to fork an article on relativistic effects until that section grows too large for the main article. At present it's about zero bytes, so there's no rush. --PeR (talk) 18:25, 8 August 2008 (UTC)

Hi Per: I am not concerned over the length of the present article, but would like to shunt discussion of the polar coordinate version away from this page, where frankly I don't care what happens to it. Brews ohare (talk) 22:33, 8 August 2008 (UTC)

The change proposed by The Anome, which received supportive comments from PeR and myself, and dissenting comments from Brews and Wolf, was significantly different than what Wolf has now implemented. (The proposal was to create an article called Centrifugal Forces in Rotating Frames, and then the article on simply Centrifugal Force could adopt a more comprehensive approach reflecting the full range of views in the published literature.) I don't think that 3:2 constitutes consensus for the "2" position. As I understand it, Brews & Wolf are adament about excluding any mentions (other than perhaps dismissive and derogatory ones) of the more comprehensive view of the subject of this article taken by numerous reputable reference sources. Would it be possible for Brews and/or Wolf to summarize their reason(s) for taking this position? Unless they can provide some valid justification, it seems to me that their position is prima facie contrary to Wikipedia policy. I think it would help if their answer(s) could be phrased in terms of (for example) why certain references are not actually from reputable sources, and so on, rather than in terms of "well, I think the most sensible definition of fictitious force is such and such", since, as we all know, our own personal POVs are not relevant.Fugal (talk) 17:32, 9 August 2008 (UTC)

My reasoning has been explained already. Fugal's view that a "more comprehensive" article is necessary is a ploy to include a digression on a specific use of the same term in a mathematical, rather than a physical, context. The use of the same term by the mathematically inclined to mean something else is not a reason to add an extensive discussion of this occurrence to this article, which is about physics, not about polar coordinates. Although I expect Fugal to dispute the ability to divorce this physics-related phenomena from polar coordinates, in fact that has been done in the present article by focusing upon the physics, and not upon polar coordinates. Of course, any physics phenomena can be explained in a manner independent of any specific coordinate system, for example, by the use of vector analysis. That is the approach taken. Reference to the mathematicians' use of the term in connection with polar coordinates has been made for the sake of completeness, but that is all the billing it deserves in this physics article. Brews ohare (talk) 23:43, 9 August 2008 (UTC)

I was hoping your justification wouldn't just consist of your own original research concerning what you regard as a distinction between what is "physical" and what is "mathematical". If the basis vectors of a coordinate system change in time, you call the resulting terms appearing in the equations of motion "physical", whereas if the basis vectors of a coordinate system change in space, you call those same terms arising in the equations of motion "mathematical". This is unfortunately an only too familiar attitude among a certain well-recognized kind of individual, who, when pressed to justify his beliefs, falls back on meaningless and misguided assertions of a profoundly important distinction (which, alas, only he can see) between "physical" and "mathematical", e.g., the Lorentz transformation is dismissed as being "only mathematical, not physical", and professional physicists are accused of failing to distinguish between mere math and genuine physics. Experience has shown that it is never productive to engage such individuals in a discussion of their views, so I don't propose to do that here. I will just repeat my request that you present a justification of your position, not in terms of your personal beliefs and Point of View, but in terms that address the existing literature in reputable published sources. Thanks.Fugal (talk) 02:50, 10 August 2008 (UTC)

Fugal: Well you have indeed raised the level of discourse. I cannot improve upon your own rhetoric: " This is unfortunately an only too familiar attitude among a certain well-recognized kind of individual, who, when pressed to justify his beliefs, falls back on meaningless and misguided assertions. Experience has shown that it is never productive to engage such individuals in a discussion of their views. I will just repeat my request that you present a justification of your position, not in terms of your personal beliefs and Point of View, but in terms that address the existing literature in reputable published sources. Thanks." Despite your excellent advice just quoted, I have made another effort below. Brews ohare (talk) 19:16, 10 August 2008 (UTC)

I don't understand your point. My position is entirely based on the existing literature in reputable published sources, several of which have been provided, in which is presented a view of the subject of this article that is presently not accurately represented in the article. My position is that this is not an insignificant minority or fringe viewpoint, but is in fact a view represented in a significant fraction of the literature, and hence merits inclusion (accurately) in the article. You, on the other hand, are arguing for the exclusion of this view (or a derisive POV dismissal of it), and your basis for this position is (correct me if I'm wrong here) that you believe one view is "physical" and the other view is "merely mathematical". I don't think your personal philosophical ideas about what is "physical" and what is "mathematical" constitute a valid basis for deciding what qualifies for the article. If you could cite some reputable source explaining that one view of this subject is physical and the other merely mathematical, then your position would be legitimate, but you haven't cited any such source. That's why I call your comments "original research". I don't think the attitude will get us very far. I'm trying to articular a well-reasoned argument here, and what I get in return is "I'm paper and you're glue; everything you say bounces off me and sticks to you!". Sheesh.Fugal (talk) 18:48, 10 August 2008 (UTC)

3:2 isn't a consensus at all. Look, this isn't merely a question of the editorial opinion, we're supposed to be making an informed decision about what is NPOV, based on evidence. For example, I did a google on 'centrifugal force', ignoring the wikipedia I got:

• [3] - talks about rotating reference frames
• [4] rotating reference frames
• [5] rotating reference frames
• [http://hyperphysics.phy-astr.gsu.edu/HBASE/corf.html[ rotating reference frames/mach principle
• [6] doesn't exist at all
• [7] rotating reference frame
• [8] copy of columbia encyclopedia reactive centrifugal force
• [9] dunno, vague "inertia"
• [10] rotating reference frame
• [11] spam
• [12] not specified, reactive?
• [13] fictitious doesn't really exist
• [14] rotating frames of reference

Feel free to check these to make sure I've classified them correctly, and do your own googles or other kinds of searches.- (User) WolfKeeper (Talk) 00:00, 10 August 2008 (UTC)

You say "3:2 isn't a consensus at all." Could you expand on that comment? Your views were in the minority, and yet you went ahead and made your change, so I pointed out that you couldn't justify your edit based on a clear consensus of the editors. Now your answer is to tell me that "3:2 isn't a consensus at all". I know it isn't a consensus, even less so for the 2 position than for the 3 position, and yet you implemented an edit based on the 2 position. How do you justify this?

As to your web search results, you unfortunately overlooked one or two, such as

http://math.ucr.edu/home/baez/classical/inverse_square.pdf

http://www.scar.utoronto.ca/~pat/fun/NEWT3D/PDF/CORIOLIS.PDF

http://www-math.mit.edu/~djk/18_022/chapter02/section04.html

http://www.phy.umist.ac.uk/~mikeb/lecture/pc167/gravity/central.html

http://www.cbu.edu/~jholmes/P380/CentralForce.doc

http://www.myoops.org/twocw/mit/NR/rdonlyres/Mechanical-Engineering/2-141Fall-2002/1BEBB815-1441-4698-8D09-3C0E378291F3/0/spring_pendulum.pdf

This is just from about 60 seconds worth of browsing. All of these explicitly present as "centrifugal force" the term arising from the basis vectors changing in space, e.g., stationary spherical, cylindrical, polar, parabolic coordinates. I also found a cite that carefully stated centrifugal force appears only in rotating coordinates, and then proceded to derive the centrifugal force in terms of stationary polar coordinates, so one has to be careful to distinguish what people think they are doing from what they are actually doing.

Careful here. I just gave the top-hits from google, because it's the most unbiased way I know to quickly get a feel for what most people think on a subject (using multiple search engines would improve this further). Clearly there are a variety of views, but the majority are to do with rotating reference frames. Absolutely, absolutely you can come up with many references that talk about other ways of dealing with it, but rotating reference frames seems to be the most common, and this is compatible with the wikipedia's article layout. Your links above don't deal with the commonality angle at all.- (User) WolfKeeper (Talk) 15:46, 10 August 2008 (UTC)

But in this game of dueling web links you are at a distinct disadvantage, because clearly there is a sizeable set of links that advocate each of the views under discussion, i.e., those that think only when the basis vectors change with time can the accelerating terms properly be called fictitious forces, and those who think it is just as legitimate to regard as fictitious forces terms arising from the basis vectors changing in space. This is consistent with my position here; I content that both views of the subject are represented by a significant portion of the reputable sources. Your position, on the other hand, is that ONLY sources that agree with your POV exist, so your task is to deny the existence of all the sources, both on the web and more importantly in published texts, that present the more comprehensive and unified view of the subject. I don't see how exactly you expect to be able to prove the non-existence of things whose existence is really beyond dispute... but I'm keeping an open mind. In view of all the published texts that have been cited, along with the web pages (and the lists could be extended indefinitely), could you tell me how you justify your belief that what I call the more comprehensive view of this subject is NOT represented by a significant number of reputable sources?Fugal (talk) 02:50, 10 August 2008 (UTC)

You'll have to point towards where I made any such claim, because I have never done so, and that your claim that that my "position, on the other hand, is that ONLY sources that agree with your POV exist, so your task is to deny the existence of all the sources", here your assumption of bad faith could not be made any clearer. Indeed I have added links to the articles to other definitions and have discussed the commonalities and differences endlessly.- (User) WolfKeeper (Talk) 15:46, 10 August 2008 (UTC)

Ironically, it was my assumption of good faith that led me to infer that you believe the more unified and comprehensive view is not represented in a significant fraction of the literature. According to Wikipedia policy, the only justification for excluding some view of a subject is if that view is either not to be found in a verifiable reputable source or is only found in an insignificant fraction of the literature (i.e., "held by only one person or a small number of people"). Since your position is that the more comprehensive view is to be excluded from the article (or dismissed as ridiculous sophistry, as it is in the present blatently POV note in the article), I inferred that this was because you, in good faith, were following Wikipedia policy. If I was wrong about that, and if in fact you are trying to keep this view of the subject out of the article even though you acknowledge that it is the view taken by a significant part of the reputable literature on the subject, then I stand corrected. But in that case I think your edits are contrary to Wikipedia policy. Am I missing some subtlety of your position that somehow makes it justifiable?Fugal (talk) 18:33, 10 August 2008 (UTC)

This is not about views, this is about article scope, which in turn is to do with the definition. Since the most common technical definition of the term 'centrifugal force' is to do with rotating frames of reference, the article on that subject should be found here. Your allegedly 'more comprehensive views' are in no way excluded from the wikipedia, and please feel very free indeed to create such an article or add it one other than this one, and I'm sure we would happily link it from this one.- (User) WolfKeeper (Talk) 23:47, 10 August 2008 (UTC)

If you don't mind an outsider's opinion - Statements such as "create such an article or add it one other than this one" imply a sense of ownership in this article, which is understandable given the lengthy history with David Tombe, but not advisable. I think Wolf and Brews should be more willing to accept input from non-fringe, sourced opinions provided by other editors. Also, we already have enough forks from this article; further forking isn't necessary. Plvekamp (talk) 01:20, 11 August 2008 (UTC)

I honestly don't think there's any forks right now at all, nor should there be. If you look a term up in the dictionary, and there's 3 different definitions, then there should be 3 different articles. That's essentially the primary difference between an encyclopedia (which has one article per definition) and a dictionary (which has one article per term). Failure to understand this can cause problems with structuring as well as totally unnecessary battles.- (User) WolfKeeper (Talk) 01:56, 11 August 2008 (UTC)

It's also necessary, but not sufficient to have sourced opinions when editing. We also have to deal with questions of undue weight. And again, failure to understand how some neat idea or other is perhaps being given undue weight is very frequently highly problematic. Still, a well sourced argument should nearly always be included somewhat if it's in the scope of the article.- (User) WolfKeeper (Talk) 01:56, 11 August 2008 (UTC)

Well, hmmm... I really dislike the condescending tone of your replies, but I'll leave you to your views. I still think it might be best for you and Brews to take a break and let some of the other competent editors have a chance. This talk page is a battlefield, and it shouldn't be. Plvekamp (talk) 03:05, 11 August 2008 (UTC)

There is no tone.- (User) WolfKeeper (Talk) 03:15, 11 August 2008 (UTC)

The Anome made a good suggestion, which was to put the treatment that focuses on rotating coordinates into an article entitled "Centrifugal force in Rotating Coordinates", which would then allow the article on "Centrifugal Force" to be more representative of the full range of published views of this subject. I think you're trying to appropriate the top-level name ("Centrifugal Force") for the particular definition of centrifugal force that is of most interest to you, and even restricting it further to one particular view of the fictitious force definition, and relegate the views of that subject that appear in other reputable sources to subsidiary articles, refering to them from this main article with dismissive back-of-the-hand derision. I don't think that is editing in good faith, and I don't think it conforms with Wikipedia policy. The suggestion of The Anome, which received supporting comments from PeR and myself, was more suitable (in my opinion). The "voting" was 3:2 in favor of that proposal over yours and Brews's, but you went ahead and carried out your proposal. I can only repeat that I don't think your edits are justified under Wikipedia policy.

Surely it's not indicative of good faith to try wiggling out of Wikipedia policies, which require accurately reflecting all verifiable views on a subject, by simply declaring that you aren't trying to exclude views, you're just trying to exclude definitions. Please. That argument might have some validity for distinguishing between, say, the reactive force and the fictitious force, but it’s the height of sophistry to try to apply that argument to a restricted view and a more comprehensive view of the fictitious force interpretation. If one "definition" of a topic completely encompasses and subsumes another, to say that the more comprehensive definition is to be excluded from the top-level article on the subject is rather odd. If anything, the more restricted view should be relegated to a subsidiary article. This would seem (to me) to be more rational, and apparently the majority of editors agree.

This is just your normal weasel worded nonsense. The topic and article scope is determined by the definition. If there is more than one definition there is simply more than one article. The definitions here are varied, and this article currently covers the most common definition and hence is the one that people get when the type 'centrifugal force', and I have provided evidence of that above. If you wish to cover other definitions then you need to create or edit new articles.- (User) WolfKeeper (Talk) 09:44, 11 August 2008 (UTC)

Look, I will extend to you the same offer you extended to me. (Please excuse the tone of the following... they are your words.) “Your views are in no way excluded from the Wikipedia, and please feel very free indeed to create such an article or add it to one other than this one, and I'm sure we would happily link it from this one.” How does this proposal strike you? Fugal (talk) 05:05, 11 August 2008 (UTC)

I already did create this article, I defined it and edited it over a long period, and Brews did even more work to it. We did the work. You didn't. But nevertheless I'm quite happy with your suggestion.... but if and only if you can show that the current definition isn't the most common and most notable definition.- (User) WolfKeeper (Talk) 09:44, 11 August 2008 (UTC)

Just out of curiosity, are you consciously mimicking Coriolanus there?

Anyway, there are some genuinely disparate concepts that go under the name “centrifugal force”, but there are also single concepts that have multiple distinct but equivalent (or overlapping) definitions. If a certain individual thing can be (and often is) defined in different ways, these represent different views of the same subject. This is not the same as (say) the difference between the various definitions of “bark”, where one definition refers to the sound of a dog, and another refers to the skin of a tree, and another refers to a boat. Those are distinct meanings, distinct subjects, and properly would deserve their own articles. But when talking about "centrifugal force", defined as an extra acceleration term (treated as a force) that arises when equations of motion are expressed in terms of certain coordinate systems, we don’t really have such different subjects. The various ways of defining the “fictitious force” concept are really just different ways of viewing one and the same subject. It just so happens that one definition, while entirely encompassing the other, also unifies it in a conceptually coherent way with a somewhat larger range of things that also, fortuitously, go under the name of centrifugal force.

Compare this with coriolis force, which is mentioned in the current article 35 times. No one claims that coriolis force is the same as centrifugal force (by any definition), so why is it in this article? Well, presumably it’s in this article to provide context for understanding centrifugal force by comparing and contrasting it with similar and related concepts. So, even though all the discussion of coriolis force in this article is arguably off-topic, no one objects, because it is understood to be providing useful context. But surely it is even more useful to point out that centrifugal force (and coriolis force) are just special cases of a more general unified concept, one that explains how they fit in the context of all fictitious forces, and is consistent with the more sophisticated literature on the subject, and that unifies them with other concepts that also (fortuitously) happen to be known in many reputable sources as “centrifugal force”. Surely if all the discussion of coriolis force is justified based on providing useful context for understanding, then this more fundamental context is even more justified.... and yet the article breathes not one word about it, except to mock it derisively, based on misunderstanding and some original research notion about fictitious forces being "physical". (Apparently the definition of “physical” is “Whatever Brews says it is”.) I really think you two guys should take a break. Read the Wikipedia policy on “ownership” and take the advice to heart.Fugal (talk) 19:56, 11 August 2008 (UTC)

< outdent ------------------------

IMHO any completely general treatment needs to be in fictitious forces.- (User) WolfKeeper (Talk) 21:44, 11 August 2008 (UTC)

And I hope you're not serious about coriolis force being offtopic here. We're allowed to talk about directly related topics in an article and how they relate, and centrifugal force and coriolis forces go around in pairs- they're joined at the hip. And notably the polar coordinate coriolis force and the rotating reference frame coriolis forces are surprisingly different. In polar coordinates the coriolis term is always strictly rotational, whereas in rotating reference frames it can point in any direction at all perpendicular to the frame rotation axis. You'll also notice that there's only one definition of the coriolis force in the coriolis effect article. If you were being in any way consistent you should be commenting on that talk page as well.- (User) WolfKeeper (Talk) 21:44, 11 August 2008 (UTC)

You're misunderstanding his point. He's pointing out how the coriolis force comments provide context, not proposing their removal from the article. His "why is it in this article?" question is rhetorical, not literal. Fugal's not a crank, he has valid concerns. I wish you guys would quit trying to bash every point he makes. Again, I point you towards WP:OWN. Plvekamp (talk) 00:41, 12 August 2008 (UTC)

Nah, not me anyway. It all comes down to scope really. Personalities are usually irrelevant in the long run, the wikipolicies usually work it out in the end.- (User) WolfKeeper (Talk) 03:34, 12 August 2008 (UTC)

Evidently you didn't read what I wrote. I carefully explained the rationale for including comments on the coriolis force in this article (for context and relationships), and you responded by informing me that there are reasons for including comments on the coriolis force in this article. That's non-sequitur #1.Fugal (talk) 03:47, 12 August 2008 (UTC)

That's not a non-sequitor, you were arguing that there was no true relationship between coriolis force and this article, but that there is a stronger one to other forms of centrifugal force. For inertial polar coordinates, the main relationship is a similar name, and the equation looks similar, but really isn't, the symbols mean different things. I don't think that that argument can be sustained. It's at best a family relationship, but coriolis and centrifugal are cohabiting.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

But the core of your argument is that: If a certain individual thing can be (and often is) defined in different ways, these represent different views of the same subject. This is not the same as (say) the difference between the various definitions of “bark”, where one definition refers to the sound of a dog, and another refers to the skin of a tree, and another refers to a boat. Those are distinct meanings, distinct subjects, and properly would deserve their own articles. But when talking about "centrifugal force", defined as an extra acceleration term (treated as a force) that arises when equations of motion are expressed in terms of certain coordinate systems, we don’t really have such different subjects.

I honestly think it's a good definition. It's completely wrong for this article though, if necessary we should move this article to one side, rewriting this article to try to meet it would be nuts. There's also the question of article layout within the wikipedia- what article the users get when they search for particular terms. I personally think that the current choice is a good one.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

Then you expounded on how centrifugal and coriolus force are "joined at the hip" and therefore must be treated together, but in the same message you informed us of your humble opinion that any "general treatment" needs to be in the fictitious force article. It's perfectly clear that what you really mean is, YOUR general treatment (mixing centrifugal and coriolus forces willy-skelter) is fine for this article, but the general treatment of centrifugal force contained in the published literature must be excluded from this article. So that's non-sequitur #2.Fugal (talk) 03:47, 12 August 2008 (UTC)

It's not my treatment, it's a perfectly standard treatment, and we're knee-deep in sources that use it, and it appears to be the most common treatment.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

Then you scold me for not correcting the mistakes that you and Brews have spawned into a multitude of other related articles. You mentioned the article on the coriolis effect (which is actually less relevant for a variety of reasons), but you might also have mentioned the article on Inertial Frames, etc. But is it really MY fault that you two have spread your sophomoric misunderstandings into all these articles? Science crackpots are always more energetic in the promotion of their crackpottery than other people are in the debunking of it. For you to berate me for not having corrected more of YOUR errors, and to attribute this to "inconsistency" on my part, well, I'd call that non-sequitur #3.Fugal (talk) 03:47, 12 August 2008 (UTC)

You've never actually edited anything, any article in the wikipedia have you Fugal?- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

As to your lastest original research on coriolus force in polar and rotating coordinates, forgive me, but considering that you announced just a few days ago that there is no such thing as three-dimensional polar coordinates (!), I hardly think you're qualified to be lecturing on this subject. Suffice it to say that you have no clue what you're talking about. And let me remind you again that these Discussion pages are not for the discussion of the subject of the article, they are for discussion of editing the article. Your original research (like that of Brews) is irrelevant. Fugal (talk) 03:47, 12 August 2008 (UTC)

I said that the treatments were different, 3D here, 2D in polar coordinate system. Sure you can generalise, but nobody had, and nobody has since come up with a 3D treatment either, it's not difficult, but nobody has. And what original research? The coriolis term in polar coordinates applies only to the angular term, are you seriously arguing that it doesn't? The arguments against doing OR don't apply in talk, we're supposed to be doing research for the article. And you're continuing to fail to assume good faith.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

Let's just take stock for a minute: You continue to promote original research, exclude views of the subject that are well represented in a large fraction of the literature on the subject, make edits against the majority of editors, and assert ownership of this article, all in violation of Wikipedia policy. Not bad for a day's work.Fugal (talk) 03:47, 12 August 2008 (UTC)

Let's just take stock for a moment, we're discussing what to do about a difficult topic/article structure in a talk article and OR is perfectly OK in talk (I haven't engaged in it anyway), I've excluded no views at any time, and the wikipedia is not a democracy it works on consensus.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

Quite frankly, the more I look at this, the better having more articles looks. Some people have called this fragmentation, and perhaps expect that there would be massive duplication, but in reality that rarely happens, the hypertext nature of the wikipedia makes it easy to link to where detailed treatments are. There's also the user-centered point that people are usually looking for a particular topic that is for them, at their current education level and purposes, and right now we've not catered well to those different levels, and using a more general definition in this article would only make that worse, generality always implies greater complexity, even if it ultimately looks simpler.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)

Centrifugal force as a physical concept, and as mathematics

Fugal characterizes the view of the present article that centrifugal force is a concept of physics is "original research". That arbitrary statement is rejected by all the citations in the article. There also is another meaning for "centrifugal" sometimes introduced in the limited context of polar coordinates as a mathematical device in that coordinate system. This different usage also is recognized in the article, but is obviously not the subject of the article. A full discussion of this other use is in the article on polar coordinates. What else needs to be said? Do we need a google search to count usages for each interpretation? This article is about the physics, not about math. Does an article on bridgework refer to the Golden Gate?

According to Fugal: "If the basis vectors of a coordinate system change in time, you call the resulting terms appearing in the equations of motion "physical", whereas if the basis vectors of a coordinate system change in space, you call those same terms arising in the equations of motion "mathematical"." And in later discussion, Fugal says: "…those that think only when the basis vectors change with time can the accelerating terms properly be called fictitious forces, and those who think it is just as legitimate to regard as fictitious forces terms arising from the basis vectors changing in space.". This characterization is incorrect. The contrast is not between different types of coordinate system (time varying vs. space varying, or whatever), but between a coordinate system (which provides a mathematical description of observations in space and in time) and a state of motion; and how that state of motion affects one's observations. Thus, an observer in an inertial frame can use a polar coordinate system, and so can an observer in a non-inertial frame. And both also can avoid doing so altogether and use Cartesian coordinates, or arc-length coordinates, or use vector analysis. Whatever approach they choose to describe their observations, it may be pointed out, the inertial observer finds only "real" forces enter Newton's laws of motion (forces that originate between physical bodies), while the non-inertial observer finds it necessary to add fictitious forces, among them the (physical) centrifugal force of this article. That (physical) centrifugal force is not the so-called "fictitious force" of mathematical manipulation. The so-called "fictitious force" of mathematical manipulation occurs for either observer if they choose polar coordinates, and is an artifact of polar coordinates, not a consequence of the state of motion of the observer. If citations are needed to support these explanatory remarks, please see the article proper.

As a mathematical point, the acceleration in polar coordinates is

${\frac {d^{2}\mathbf {r} }{dt^{2}}}=({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\mathbf {r} }}+(r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}){\hat {\boldsymbol {\theta }}}=({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\mathbf {r} }}+{\frac {1}{r}}\quad {\dot {\overbrace {r^{2}{\dot {\theta }}} }}\quad {\hat {\boldsymbol {\theta }}}$

The term $r{\dot {\theta }}^{2}$ is sometimes referred to as the centrifugal term as a mathematician's idea of picturesque vocabulary. In this equation, one component points in the radial direction (unit vector ${\hat {\mathbf {r} }}$) and the other component in the direction normal to this one (unit vector ${\hat {\boldsymbol {\theta }}}$). These two directions are not along and normal to a particle's trajectory except in unusual cases, such as circular motion about a fixed center coinciding with the origin of the polar coordinates. However, the (physical) centrifugal force (from the particle's viewpoint) is always normal to the particle's trajectory; in general, not in direction ${\hat {\mathbf {r} }}$. Consequently, regardless of the mathematical conceit that the polar equation terms include a "centrifugal term" that terminology is at best poetic license from a physical context based upon the moving particle. Of course, if the polar coordinate system is that of an inertial observer, there is in fact zero (physical) centrifugal force; despite whatever the mathematical conceit chooses to call "centrifugal"; rather, there is a (physical) centripetal force, which is normal to the path of the particle, and not directed toward the center of polar coordinates; that is, unrelated to either term in the mathematical expression for acceleration above. Again, the mathematical conceit is only poetic license.

Again, none of this explanatory material is controversial. For citations, see the articles on polar coordinates, centripetal force, fictitious force and of course centrifugal force. I have had a lot to do with these articles, but I am not citing myself: rather, I'm suggesting you look up the citations in these articles.

Although planar polar coordinates are used in the mathematical example above, the same ideas apply to spherical or cylindrical coordinates. Only the form of the mathematical terms alters; the variously identified, mathematically picturesque "centrifugal" terms still are at best only very indirectly related to the (physical) centrifugal force, except for particular trajectories. Brews ohare (talk) 19:21, 10 August 2008 (UTC)

Let me start by saying that, notwithstanding the attempts to suggest an affiliation with published sources, the narrative above constitutes original research. Brews has energetically filled several Wikipedia articles with his own POV on a set of related subjects, and is trying to leverage off of those to continue enlarging his empire of confusion. I really think it's time for some fresh air on these topics. Plenty of Brews's statements are uncontroversial, but also have no bearing on the issue at hand. The only relevant passage in the above rambling is:

“The contrast is not between different types of coordinate system … but between a coordinate system (which provides a mathematical description of observations) and a state of motion; and how that state of motion affects one's observations.”

That’s utterly incorrect, and contains so many implicit fallacies that it's hardly worth de-constructing it. Look, the “observations” (i.e., raw sense impressions) of an observer are related only indirectly to the higher level conceptual framework of three-dimensional Euclidean space plus time. There’s a huge epistemological distance between primitive “observations” and “states of motion in space and time”, which would take a long time to explain. Fortunately that’s unnecessary, because the theory of epistemology is irrelevant to this discussion. The state of motion of an “observer” (or even the presence of an observer) is utterly irrelevant to the concept of a fictitious force. Every reputable source explains that fictitious forces arise when motions are described in terms of certain kinds of coordinate systems. Needless to say, the very same motions can be described in terms of infinitely many different systems of coordinates, and in some of those systems the absolute accelerations will equal the second time derivative of the space coordinates, whereas in others the absolute acceleration will consist of that second derivative plus some additional coordinate-dependent terms. These are the terms that, if it’s convenient, we may choose to bring over to the other side of the equation and pretend they are “forces”, hence fictitious forces. Brews’s ideas about “observers” versus coordinate systems are original research and don’t belong in Wikipedia. (Those ideas also happen to be quite wrong, but it’s pointless to argue that here. It suffices to say they are original research and hence irrelevant to this discussion.)

Maybe I should also point out that the business about things in curvilinear coordinates only corresponding to fictitious forces in certain specialized configurations is totally bogus. As explained in (for example) Beers and Johnston’s Statics and Dynamics, “The tangential component of the inertia vector provides a measure of the resistance a particle offers to a change in speed, while its normal component (also called centrifugal force) represents the tendency of the particle to leave its curved path.” In general, the inertia vector represents the “inertial forces”. In rectilinear unaccelerated coordinates the inertia vector of a particle always points along the “straight lines” of the coordinate system, so there are no fictitious forces. But if the coordinate system is accelerated or non-rectilinear or both, the “straight lines” of the coordinate system veer off from the inertia vector. If we choose to adopt the fiction that the “straight lines” of our coordinate system are actually straight, then we conclude that the inertial particle is actually accelerating, and we attribute this to the presence of fictitious forces. This is in no way limited to special configurations. We merely consider the inertial tangent vector at each point along the path of the particle.

Furthermore, even under the limited partial approach to dynamics that Brews favors, he understates the ambiguity, because the axis of rotation of a coordinate system (or an observer if you wish) may be continuously changing, both in position and orientation, so the decomposition of the acceleration terms into easily classifiable components involves just as much complexity as it does when basis vectors change in space.

One last point: The equality of the fictitious forces in cases when the basis vectors are changing in time versus when they are changing in space is not at all just a fortuitious coincidence. For example, if a particle is moving absolutely in a circle, and we describe it in terms of a coordinate system rotating at the same speed as the particle, then the fictitious force is due to the changing basis vectors with time. But if we describe the same particle in terms of stationary polar coordinates, in which the direction of the basis vectors change in space, we see that the particle is changing its spatial position with time, and hence the relevant basis vectors are (again) changing in time, and we arrive at exactly the same acceleration term. It’s just two ways of looking at exactly the same thing. But the main point is that this isn’t just Fugal talking, this is the view of the subject taken in a very sizeable fraction of the published literature on the subject.63.24.52.50 (talk) 22:03, 10 August 2008 (UTC)

I am afraid 63.24.52.50 has made only a lot of pronouncements that do not withstand scrutiny and have not been supported by citation. In effect, 63.24.52.50 has not carefully addressed the detailed discussion he attacks (nor the various articles) in an orderly manner. That does not encourage the view that real discussion can take place.

I point at one sentence from the above rant: "The state of motion of an “observer” (or even the presence of an observer) is utterly irrelevant to the concept of a fictitious force." This statement contradicts virtually all references cited in centrifugal force, and if it really is what this editor means, suggests an ignorance of the subject that is quite amazing. Here is only one citation (of many from googlebooks) that contradicts this remark Borowitz–A Contemporary View of Elementary Physics: "The effect of his being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…". Brews ohare (talk) 05:26, 11 August 2008 (UTC)

Here's just one more high-quality citation (on top of the seven I've already provided). Take a look at the very clear discussion of this topic in Michael Friedman's "The Foundations of Space-Time Theories", Princeton University Press, 1989. I've not doubt that you will find his ignorance of the subject as amazing as mine.

I looked up Friedman's book, but unfortunately it is not excerpted on googlebooks, so I cannot say whether his understanding or your interpretation of his words will prove the more amazing. Brews ohare (talk) 16:18, 11 August 2008 (UTC)

You say I have not carefully addressed your detailed discussion, but that's not true, I clearly explained above why your discussion is wrong. And your statement that my comments are unsupported by citation is also false, as I'm simply re-iterating the statements for which numerous citations have already been provided. Furthermore, these pages are not for discussions of the subject of the article, they are for discussion of the article itself, focusing on material from verifiable sources. The things that I'm "attacking" are things like your statement in the article where you say the unified and comprehensive modern view of fictitious forces "has no connection to the physics", and that it is purely mathetical rather than physical, or some such nonsense. That is original research (not to mention wrong), and does not belong in the article. I'm not interested in trying to convince a crackpot that he's wrong... I know very well that it's impossible to do. I'm just trying to bring Wikipedia policies to bear, to eliminate the original research that you have inserted into this article. As far as I can tell, you and Wolf are violating those policies, and acting as if you "own" this article. You don't.Fugal (talk) 05:41, 11 August 2008 (UTC)

I have provided chapter and verse on these matters; you have not. Brews ohare (talk) 16:18, 11 August 2008 (UTC)

Brews this assertion of yours: Of course, if the polar coordinate system is that of an inertial observer, is somewhat illustrative of the argument here. The thing is polar coordinates do not necessarily refer to an inertial frame.(TimothyRias (talk) 08:46, 11 August 2008 (UTC))

The word "if" means that the assumption is not necessary, but suppose it were true. Brews ohare (talk) 16:08, 11 August 2008 (UTC)

As I've explained above the physical notion of a frame is inherently local. (this is somewhat obscured by the Poincare symmetry of flat space but is also true in flat space.) Besides an global choice for an inertial frame, you can also make a other natural choice for the local frames. I like to refer to this as the "Muslim" frame choice, namely the one that is always oriented in the direction of a central point (Mecca), in this choice the centrifugal term in the polar coordinates gets a very clear physical interpretation as the centrifugal force. As for your assertion that the centrifugal term in polar coordinates "only arises as a result of mathematical differentiation." Yes, thats true, but the same is true for the centrifugal term in a rotating frame of reference. The centrifugal force always arises as extra terms introduced in the covariant derivative. (TimothyRias (talk) 08:46, 11 August 2008 (UTC))

In an inertial frame of special relativity, which includes Newtonian mechanics as a special case, there is zero physical centrifugal force, regardless of the coordinate system selected. There is, however, inward normally directed centripetal force if the observed trajectory is curved. In general relativity, I do not understand the theory well enough to say exactly what the situation is. However, general relativity is outside the scope of the article. Do you need citations to support my statement here? Brews ohare (talk) 16:08, 11 August 2008 (UTC)

In general relativity (or in any covariant approach to classical mechanics) there never is any physical centrifugal force. (there also is no physical gravity) All terms normally called centrifugal force are just acceleration terms for some particular choice of coordinates. (or alternatively choice of local frames, coordinates are not really necessary but tend to be a convenient way to define the local frames.) And this really is not beyond the scope of this article because this epistemoligical lesson (which doesn't really need GR/the einstein equations) has long since trickled back into out understanding of fictitious forces. Among others this has lead to the realisation that there is really logical difference between the centrifugal force as it appears in rotating frames and as it appears in polar coordinates. Both may be interpretated (in that is all that is happing; interpretation) as fictious forces resulting from a certain choice of local frames and insisting that the connection remains trivial. (TimothyRias (talk) 08:32, 12 August 2008 (UTC))

Timothy: To expect the notions of general relativity to be understandable by use of a few sentences and no background or mathematics is to make a mockery of a lifetime's work by many. I cannot see how introduction of these concepts in an unsupported zero-context fashion can assist the reader without general relativity background. To do justice to such a treatment, you should write a stub about it, where appropriate space and citations can be presented. It can be linked to the present article for those with the interest and capacity to pursue this topic. Brews ohare (talk) 14:58, 12 August 2008 (UTC)

My main point is that you should not be stating (here or in the polar coordinates article) that there is no physical connection between the centrifugal term in polar coordinates and that in a rotating frame, as physically they are in fact pretty much the same. You seem very keen on stressing that there is no connection. I'm not sure why. A much simpler approach would be to leave it in the middle what the connection between the two is and simply not that both are the centrifugal force. This is the approach of many notable textbooks, so why should it be so bad for wikipedia. (TimothyRias (talk) 15:53, 12 August 2008 (UTC))

Within classical mechanics the two concepts are completely different. I cannot say what happens in general relativity. However, it does not seem to serve the reader to suggest they are the same concept in an article that has no pretensions at general relativity, when in this limited context the two ideas are totally separate, both logically and physically.

That clear distinction makes me wonder if you are not smearing together separate ideas in general relativity as well, where matters are much more likely to become murky as not only the observer has the (mathematical) opportunity to change local coordinate systems, but space-time also is local and curvilinear for physical (not mathematical) reasons. The two aspects might become coupled, but I frankly am skeptical that they are truly identical even in this context. For example, the Schwarzschild solution uses polar coordinates, showing that a choice of coordinate systems still is possible in general relativity, and space-time geometry does not tie one's hands entirely. After all, it would be odd if matters that were logically distinct and with different origins (arbitrary naming in the mathematical formula for acceleration of a few coordinate-system-dependent terms that are independent of any particular state of motion vs. physics involving state of motion) were to become exactly the same thing in a more general context.

Anyway, that connection is best left for a separate article where the merging of two unrelated concepts can be shown to occur as gravity becomes stronger (supposing that actually to be the case). Brews ohare (talk) 18:58, 12 August 2008 (UTC)

With this statement as background, in a curvilinear coordinate system, as you note, there is always some metric tensor, not just the simple diagonal tensor of ones found in the Cartesian system. These functions invariably lead to "fictitious forces" in the picturesque mathematical sense. However, they do not lead to physical centrifugal force in inertial frames. The polar coordinate example spelled out in detail here is a particular example with everything worked out in detail. Do you need citations on this? Brews ohare (talk) 16:08, 11 August 2008 (UTC)

Your concept of "physical fictitious forces" is pure original research, as is your belief that there are “physical fictitious forces” and “mathematical (or poetic) fictitious forces”. I don’t believe you can cite any reputable source to back up this “physical versus mathematical” dichotomy. This alleged dichotomy is, of course, quite common among a certain class of original thinkers, but it doesn’t appear in reputable sources, so it doesn’t belong in Wikipedia. All reputable sources agree that fictitious forces are not really forces at all, let alone “physical forces”. They are extra acceleration terms (beyond the second time derivative of the space coordinates) that appear when the absolute acceleration of an object is expressed in terms of various coordinate systems. There's nothing more or less "physical" about fictitious forces depending on whether they are due to basis vectors changing in time or in space (or both). You've been provided with numerous high-quality sources that explain all this. I don't think your repeated denials, based on your original research regarding "physicality" versus "mathematicality", are very productive.Fugal (talk) 19:28, 11 August 2008 (UTC)

We may have a semantic problem here: I have used the terms "physical" and "mathematical" to distinguish between the fictitious force due to a state of motion and that fictitious force due to the mathematical exercise of identifying a few terms in the mathematical expression for acceleration as expressed in polar coordinates regardless of the state of motion. I thought this meaning was pretty clear, but maybe now it is is clearer still? So your remarks about "All reputable sources agree that fictitious forces are not really forces at all" are wide of the mark, as I do not disagree at all with the fact that what I have called physical fictitious forces are fictitious forces in the sense of state-of-motion, eh? However, I believe your point is that both the type of fictitious force I have called "physical" and the type I have called "mathematical" are the same. I already have provided you with citations that indicate that they are not the same, and that what I have called "physical fictitious forces" that is , fictitious forces related to state-of-motion disappear in inertial frames, while the "mathematical" type of fictitious forces do not. Below I repeat an exchange with a citation that you have chosen to ignore:

Fugal: "The state of motion of an “observer” (or even the presence of an observer) is utterly irrelevant to the concept of a fictitious force."

Brews_ohare: Here is only one citation (of many from googlebooks) that contradicts this remark Borowitz–A Contemporary View of Elementary Physics: "The effect of his being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…".

Here's a few more: "The reason the centrifugal force is fictitious is because it involves a noninertial frame of reference" Bergethon The physical basis of biochemistry

"Centrifugal force is a fictitious or "phony" force that we introduce to correct for the acceleration of our rotating frame of reference" Oliver: Collected papers

"The centrifugal and Coriolis force are called fictitious forces because they are needed only by an observer in a rotating reference frame." Armstrong Mechanics waves and thermal physics

"In a non-inertial rotating reference frame, centrifugal force is defined as a d'Alembertian inertial force, a fictitious force acting on the moving body." Sneddon Encyclopaedic Dictionary of Mathematics for Engineers and Applied Scientists

"If we insist on treating mechanical phenomena in accelerated systems, we must introduce fictitious forces, such as centrifugal and Coriolis forces." Meirovitch Methods of Analytical Dynamics

It is clear to me that these quotations directly and unequivocally contradict your claim as to the irrelevance of state of motion to the concept of fictitious forces. Brews ohare (talk) 06:11, 12 August 2008 (UTC)

Personally, I've never seen a constant speed rotating polar coordinate reference frame being discussed in a book, so I'm not sure it's particularly notable, but I've no objection to it having a section, provided it's a short one, and it's well referenced, since it would meet the definition.- (User) WolfKeeper (Talk) 10:08, 11 August 2008 (UTC)

Fugal's positions

Fugal

My position is that [the mathematical terminology for certain terms in the acceleration of a body as viewed in curvilinear coordinates] is not an insignificant minority or fringe viewpoint, but is in fact a view represented in a significant fraction of the literature.

Brews-ohare

My view is that it is not a viewpoint, but a different use of terminology. That these terms constitute a different usage is shown (in part) by the fact that these terms are an artifact of the coordinate system, and therefore appear in every state of motion, every frame of reference, in both inertial and non-inertial frames. That is not true of centrifugal force as defined in this article. As a different subject, a reference to this alternative usage is all that is needed. I believe Wolfkeeper has the same view. Brews ohare (talk) 14:41, 12 August 2008 (UTC)

Fugal

The state of motion of an “observer” (or even the presence of an observer) is utterly irrelevant to the concept of a fictitious force.

Brews_ohare

Here is only one citation (of many from googlebooks) that contradicts this remark: Borowitz–A Contemporary View of Elementary Physics: "The effect of his being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…". Brews ohare (talk) 15:55, 12 August 2008 (UTC)

Fugal

Also, the acceleration terms appearing with certain coordinates do not depend on the presence or state of motion of any observer.

Brews_ohare

My point exactly: however, centrifugal force (as used in this article) does depend on the state of motion of the observer. In Newtonian mechanics, a state of acceleration (a state of motion) identifies a non-inertial frame of reference. A citation: "If we insist on treating mechanical phenomena in accelerated systems, we must introduce fictitious forces, such as centrifugal and Coriolis forces." Meirovitch Methods of Analytical Dynamics . Brews ohare (talk) 15:37, 12 August 2008 (UTC)

Fugal

Fictitious forces are, by definition, artifacts of a particular choice of coordinate systems. They are all "mere mathematical manipulations".

Brews_ohare

In fact there are two meanings for fictitious force: one depends on the state of motion of the observer (see above) and one is a mathematical act of poetic license, applying picturesque language to certain terms that arise in the acceleration when calculated in curvilinear coordinates, without regard for the observer's state of motion. Are we going 'round and 'round here?!? Here are two quotes relating "state of motion" and "coordinate system":

We first introduce the notion of reference frame, itself related to the idea of observer: the reference frame is, in some sense, the "Euclidean space carried by the observer". Let us give a more mathematical definition:… the reference frame is... the set of all points in the Euclidean space with the rigid body motion of the observer. The frame, denoted ${\mathfrak {R}}$, is said to move with the observer.… The spatial positions of particles are labelled relative to a frame ${\mathfrak {R}}$ by establishing a coordinate system R with origin O. The corresponding set of axes, sharing the rigid body motion of the frame ${\mathfrak {R}}$, can be considered to give a physical realization of ${\mathfrak {R}}$. In a frame ${\mathfrak {R}}$, coordinates are changed from R to R' by carrying out, at each instant of time, the same coordinate transformation on the components of intrinsic objects (vectors and tensors) introduced to represent physical quantities in this frame.

— Jean Salençon, Stephen Lyle Handbook of Continuum Mechanics: General Concepts, Thermoelasticity p. 9

and from J. D. Norton:

…distinguish between two quite distinct ideas. The first is the notion of a coordinate system, understood simply as the smooth, invertible assignment of four numbers to events in spacetime neighborhoods. The second, the frame of reference, refers to an idealized system used to assign such numbers … To avoid unnecessary restrictions, we can divorce this arrangement from metrical notions. … Of special importance for our purposes is that each frame of reference has a definite state of motion at each event of spacetime.

— John D. Norton: General Covariance and the Foundations of General Relativity: eight decades of dispute, pages 835-836 in Rep. Prog. Phys. 56, pp. 791-858 (1993).

Assuming it is clear that "state of motion" and "coordinate system" are different, it follows that the dependence of centrifugal force (as in this article) upon "state of motion" and its independence from "coordinate system", while the mathematical version of "fictitious force" has exactly the opposite dependencies, indicates that two different ideas are referred to by the same terminology. The present article is about one of these two ideas, not both of them.

In summary, the article has focussed on the physical view based upon "state of motion", while Timothy and Fugal are more focussed on the mathematical manipulations within a curvilinear coordinate system, independent of the observer's state of motion. Some arguments given are more or less correct from one stance, some from the other, but the article quite properly treats the usual "state-of-motion" meaning, and refers the other to the appropriate mathematical treatment of whatever coordinate system you might like to pick, e.g. polar coordinates.

I have rewritten the section on "Aside on polar coordinates" in a way that I hope meets everybody's approval.

Brews ohare (talk) 16:54, 13 August 2008 (UTC)

Some comments on recent edits

There is something wrong with the following line introduced in one of the recent edits (at the end of first paragraph of the "Centrifugal force in general curvilinear coordinates" section):

The component of any such fictitious force normal to the path of the particle and in the plane of the path’s curvature is then called centrifugal force.

This attempt at a general definition seems to fail to include the case of a rotating reference system (the one case we all agree is the most commonly treated one), in which the centrifugal force is not necessarily normal to the trajectory of a particle. It would also include the coriolis force in such a case, since that is always perpendicular to the particles velocity. (well as long as the particle is moving in a plain perepedincular to the axis of rotation, anyway.) The sentence cites a source which I haven't been able to check. But I highly doubt that this sentence is conveying what that text was saying. (TimothyRias (talk) 14:00, 14 August 2008 (UTC))

The cited reference is Beers and Johnston’s "Statics and Dynamics", which says “The tangential component of the inertia vector provides a measure of the resistance a particle offers to a change in speed, while its normal component (also called centrifugal force) represents the tendency of the particle to leave its curved path.” In the general treatments of this subject it is recognized that the decomposition into the commonly named components called centrifugal, Coriolis, Euler, and the "fourth" fictitious force that appears in the general case becomes ambiguous. Remember, the Christoffel symbols are not even tensors, and the mapping of its various components (in terms of various coordinate systems) to the simplistic categories of centrifugal, Coriolis, etc., is ambiguous. The approach most commonly taken is as described in Beers and Johnston and represented in the article. [The ambiguity is already obvious in the simple example given in the article, of a particle moving in a circle, where the extra terms consist of mr(w+W)^2. This is the most natural and meaningful quantity, since w+W is the absolute angular speed, whereas w and W individually are artifacts of our choice of coordinate system. If we expand the expression it becomes mrw^2 + 2mrwW + mrW^2, in which case we could call mrW^2 the centrifugal force and 2mrwW the Coriolis force and mrw^2 a contribution of the fourth fictitious force. But none of these is individually meaningful (except by convention for a given choice of coordinates). Only the combination of all of them has absolute significance.]

By the way, the sentence that worries you is saying essentially the same thing as the later sentence at the end of the section (which was adapted from the pre-existing text, which talks about referring the fictitious forces to the osculating frame of a curved path. If that view was unobjectionable before, it ought to be unobjectionable now. The only difference is that I've actually provided a reference to a reputable source.Fugal (talk) 14:48, 14 August 2008 (UTC)

Centrifugal force in general curvilinear coordinates

The way this new section was introduced has a number of shortcomings, as does its content.

As to its manner of introduction, it was placed on the page without any discussion on this talk page, despite a very careful attempt on my part to resolve a number of issues on this page. My efforts, involving a simply stated contrast of views, my citations supporting these views, and my attempt to resolve these matters in a compromise, all were ignored entirely.

As to its content:

The subsection states:"This article is primarily concerned with the view of centrifugal force (and other fictitious forces) presented in introductory texts, which typically rely on intuitive though somewhat imprecise notions of concepts such as reference frames, forces, observations, and so on. In more advanced and abstract treatments of dynamics, the definitions of all these things are more general and explicit." I interpret these remarks as a dismissal of all citations opposing the author's views, which citations are in fact very numerous and include major authorities in the field such as Arno'ld, Lanczos, Landau and Lifshitz, Born, Einstein, Newton, etc. This statement is an unsupported and unsupportable slap at most of the texts on the subject, and should be deleted.

The article states: "In particular, an inertial coordinate system is defined as a system of space and time coordinates x1, x2, x3, t in terms of which the equations of motion of a particle free of external forces are simply d2xj/dt2 = 0.[51] " This definition of an inertial frame is not that of special relativity or of Newtonian mechanics. A clear counterexample is simply a frame moving with an accelerating particle: in this frame the second derivatives of position of this particle are all zero, but no-one would call this an inertial frame. The reference provided for this incorrect viewpoint is [Friedman] without page number or quotation. Given this editor's proclivity for taking things out of context, and given the clear citations for the contrary standard definition at inertial frame, this revisionist version of "inertial frame" should be removed from the page.

The article states "When equations of motion are expressed in terms of any non-inertial coordinate system (in this sense), extra terms appear, called Christoffel symbols." It is not helpful to introduce out of the blue an advanced concept like Christoffel symbols without explanation (or definition). Also, this article is not the place to introduce these technicalities, which belong (if they do belong) in a more technical article devoted to the subject of dynamics in curvilinear coordinates. It might be noted that a very large fraction of books on this subject, advanced and simple, never even mention Christoffel symbols, which apparently are not critical to the subject of centrifugal force.

The article states "Strictly speaking, these terms represent components of the absolute acceleration (in classical mechanics), but we may also choose to continue to regard d2xj/dt2 as the acceleration (as if the coordinates were inertial) and treat the extra terms as if they were forces, in which case they are called fictitious forces.[52] " The Christoffel symbols are connected to "forces" only in the limited mathematical sense of reinterpretation of mathematical terms by moving them from one side of the equation for acceleration to another, and have absolutely no connection to the state of motion of the observer. The reference cited says nothing about Christoffel symbols, and simply points out that the "mathematical device" of transferring terms from one side of an equation to the other can be described as introducing "fictitious forces". These authors are very, very careful to distinguish between the interpretation of this device in an "inertial frame" and its interpretation in a rotating frame. These sentences in this subsection distort the position of the cited source, and should be removed.

The article states "The component of any such fictitious force normal to the path of the particle and in the plane of the path’s curvature is then called centrifugal force.[53]" Timothy has objected to this statement, and Fugal's support for this statement is (i) a quotation stripped from context and (ii) some unsupported remarks about Christoffel symbols and (iii) some remarks about ambiguity and "absolute significance" in the case of circular motion that are nonsense. One problem with this sentence is that what is called centrifugal force depends on the state of motion of the observer of the particle, and so cannot be categorically given a unique definition independent of the observer.

The subsection also contains incomplete references (no links, isbn's, or page numbers), mainly to subsidiary topics (like curvilinear coordinates as an abstract mathematical topic, unrelated to physics) that are peripheral to the main thrust of the arguments. There are no definitions of terms and notation, and equations are poorly formatted.

I have removed this subsection. Before it is reintroduced, I suggest a return to the discussion opened on the talk page under the heading "#Fugal's positions", where simple courtesy demands formal response. At a minimum, there must be a proper discussion of the issues. Brews ohare (talk) 15:51, 15 August 2008 (UTC)

I think the topic is just about valid, since it discusses relationships between rotating reference frames and curvilinear reference frames which don't necessarily rotate. However, I think I would argue that this section is too large, and hence giving undue weight. I've also pruned many of the unsupported claims that rotating reference frames are in some sense vague or merely intuitive, I don't believe that, if properly defined, that that is true in any way, and as it was unreferenced, I removed it. If it can be referenced (and please make it a good reference to a factual way that this is true, rather than somebody talking hyperbolically in a book), then it may of course be reintroduced.- (User) WolfKeeper (Talk) 17:07, 15 August 2008 (UTC)

Brews, Please read WP:OWN. Demanding that people discuss additions on the talk page first is a clear sign that you have become too attached to the article. This is Wikipedia. Editors are encouraged to be bold. I am no expert at curvilinear coordinates, so I will say nothing about the actual content of the edit. --PeR (talk) 18:02, 15 August 2008 (UTC)

Mediation?

I think it might be helpful to get some fresh perspectives on this article. Several people have suggested that two individuals are showing signs of "ownership", and I have to agree. It seems that two editors have a very specific idea of exactly what this article must say, no more and no less, despite well sourced inputs from other editors. These two editors have made edits when opposed by the majority of other editors, and have repeatedly claimed ownership of this article (pointing out that THEY created it, THEY put the work into it, so any other views MUST go into other articles, not this one.) How does one go about requesting mediation in cases such as this? Fugal (talk) 21:40, 15 August 2008 (UTC)

Well, I don't know. If we were really trying to own it, we would have deleted it out of hand or moved it to a more appropriate article. I do know that you have just removed multiple largely non controversial edits, and reinserted several unreferenced statements, and made notation changes so that they don't match the rest of the article and so forth.- (User) WolfKeeper (Talk) 22:04, 15 August 2008 (UTC)

I would like to remind you that a precondition for editing the wikipedia is that other people can make changes to your work, and that you have to follow the policies on verifiability.- (User) WolfKeeper (Talk) 22:04, 15 August 2008 (UTC)

Coming from you, that is simply laughable. The only edits I have made are (1) removing the phrase referring to "out of body experiences", and (2) re-writing a brief seven-sentence ASIDE to make it more general and accurately reflect numerous referenced reputable sources. It was summarily deleted. And now you remind me that I must allow people to make edits and mind verifiability. Honestly, and I say this in complete seriousness, I believe you and Brews and genuinely lost your minds. Seriously. I think dealing with David Tombe has driven you both into clinical states of dementia. I know neither of you can see this, but others around you can see it very plainly. For your own good, take a break. Look, if it helps any, I'll promise not to have anything more to do with this article. Seriously, you two need to take a break. Seriously. S.e.r.i.o.u.s.l.y. Fugal (talk) 00:23, 16 August 2008 (UTC)

I find it impossible to reconcile your description of your edits with [15] which appears to be a general revert. And you are violating both the letter and spirit of WP:CIVIL with your above comments, and in the wikipedia this will typically overwhelm any genuine point or grievance you may have.- (User) WolfKeeper (Talk) 00:55, 16 August 2008 (UTC)

As a case in point, note the latest challenge from one of these owners: "If it can be referenced (and please make it a good reference to a factual way that this is true, rather than somebody talking hyperbolically in a book..." I think this gives a good idea of what is going on here. Since numerous references from the most reputable published sources have been provided for the views that this editor wishes to keep out of the article, he now demands that a reference be provided, but not just "somebody talking hyperbolically in a book". I think that speaks for itself. Clearly this editor will not accept any view that differs from his pre-conceived views. He simply dismisses all published works from reputable sources as "somebody talking hyperbolically in a book". And this is the more reasonable of the two owners. Some kind of mediation is badly needed here.Fugal (talk) 21:49, 15 August 2008 (UTC)

I would like to remind you that the edit you made essentially implied that it was impossible to precisely define a rotating reference frame, and the edit was unreferenced. Unreferenced material can be removed at any time in the wikipedia. If you HAVE a reference for this, then produce it and you can reinsert it.- (User) WolfKeeper (Talk) 22:04, 15 August 2008 (UTC)

Centrifugal force in polar coordinates

I have attempted to eliminate erroneous concepts that fail to distinguish between coordinate systems and reference frames. Quotations with relevant citations are given earlier on this talk page, and Fugal has been invited several times to comment. (For example, see Fugal's positions, and Fugal's sources). All the math and the statements made in the new article are non-controversial and are supported in mathematical detail by the citations. Brews ohare (talk) 22:45, 15 August 2008 (UTC)

In this connection, I suggest that the links to Stommel and Moore be followed and the work read closely. These authors are very, very careful to distinguish the cases of polar coordinates in inertial frames from that in non-inertial (rotating) frames. For example:

p. 4 "Sometimes the additional terms in the accelerations are transposed to the right side of the equation, leaving only the double-dotted terms on the left. So the acceleration terms on the right look like forces. They even acquire names such as "centrifugal force." As convenient as this may be from an intuitive, practical point of view, this transposition...can lead to confusion. ...So remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system. p. 26: "you should be very clear in your mind not to confuse the idea of a plane polar coordinate system fixed in inertial space with the idea of rotation of coordinates. This chapter is entirely tied to one particular reference frame, fixed in inertial space – so don't get mixed up now, or later when we introduce rotating axes." p. 36: This immediately gives the components of acceleration in polar coordinates, [lists equations] Remember once again that all this has nothing to do with rotating coordinate systems. We are in a polar coordinate system that is at rest with respect to the stars.... Brews ohare (talk) 23:49, 15 August 2008 (UTC)

Scope of the article & disambiguation and article name

OK, we're still battling the scope issues I think.

The disambiguation page has 4 different definitions:

• physics: In a rotating reference frame, Centrifugal force is an apparent force that seems to push a body away from the axis of rotation of the frame and is a consequence of the body's mass and the frame's angular speed.
• physics: In circular motion, the reactive centrifugal force is a real force applied by the accelerating body that is equal and opposite to the centripetal force that is acting on the accelerating body.
• physics: In polar coordinates, the apparent radial force that seems to push a rotating body away from the centre of rotation of the frame and is a consequence of the body's angular speed around the origin.
• in everyday understanding, centrifugal force is the effect that tends to move an object away from the center of a circle it is rotating about (i.e. inertia).

I'm hoping that this classification is fairly non controversial (although other people may want to add other examples of centrifugal force as well perhaps, and by all means).

I would like to move this (Centrifugal force) article to Centrifugal force (rotating reference frame) and I would propose to leave a redirect to it from Centrifugal force. This better clarifies for the users what the article is about in the name, and gives us more flexibility to change things if that should be decided later. It also gives us a specific name to link to from Coriolis effect that refers directly to the associated type of centrifugal force that that article is associated with.

I'm hoping that this too is relatively non controversial, but I welcome comments. I feel that there are people who wish to put a more general article at Centrifugal force, if anything this renaming should make that easier to do later if this type of article were created and there was consensus to change the redirect.- (User) WolfKeeper (Talk) 22:57, 15 August 2008 (UTC)

I support this change. However the description:

• physics: In polar coordinates, the apparent radial force that seems to push a rotating body away from the centre of rotation of the frame and is a consequence of the body's angular speed around the origin.

needs to be modified. It could read:

• physics: In polar coordinates, one of several terms that appear when acceleration of a particle is expressed in polar coordinates. These terms are mathematically related to the change of coordinate system basis vectors with change in the coordinates themselves.

Unfortunately, the belief advanced by some editors that these terms are closely related to physical phenomena are unsupported by close reading of the authorities on the subject. Brews ohare (talk) 23:27, 15 August 2008 (UTC)

You should discuss those IMO relatively minor changes to the terms used on the talk page of the disambiguation page if you wish to make them, and perhaps approach to the optimally imperfect phraseology can be made.- (User) WolfKeeper (Talk) 23:52, 15 August 2008 (UTC)

OK; Whether or not my view is accepted, the disambiguation I've suggested is beyond controversy, and any thoughts about physical interpretation can be left to the article proper. Brews ohare (talk) 23:54, 15 August 2008 (UTC)

Nah. ;-)- (User) WolfKeeper (Talk) 00:27, 16 August 2008 (UTC)

Given that there were no dissenting voices I have done the move.- (User) WolfKeeper (Talk) 14:33, 20 August 2008 (UTC)

Polar coordinates

While the curvilinear coordinates can be seen as a generalisation of the rotating reference frame, the polar coordinates section talks only about inertial frames of reference. It therefore isn't the same centrifugal force, and very probably needs to go.

The difference is obvious- if an object is stationary in polar coordinates, then there is no centrifugal force. In a rotating reference frame, there is a centrifugal force when the object is stationary. They are not the same thing at all, and the associated coriolis forces are completely different also, they act in different directions and are of different magnitudes.

More or less polar centrifugal force is to rotating reference frame centrifugal force as the magnetic force is to electrostatic force. And they are special cases of curvilinear equations and electromagnetism, respectively.

Magnetism and Electrostatics have almost the same form of equations, but they are completely different in reality, and the same thing applies here. Too many people aren't really getting this. Similar mathematics is just not enough.

Just like I don't think we would really want a big section on magnetism in an electrostatics article, we don't really want a big section on polar coordinates in a rotating reference frame article.

But we also don't really need too much on general electromagnetism in a magnetic article either, the curvilinear stuff is a bit OTT at the moment, it needs to mostly go in its own article, but in my opinion having something here is quite valid.- (User) WolfKeeper (Talk) 02:40, 16 August 2008 (UTC)

I am confused by your remarks. Are they about the subsection Centrifugal_force#Centrifugal_force_in_polar_coordinates? This subsection does refer to centrifugal force. It derives this force for a rotating frame, using polar coordinates in that frame. The resulting centrifugal force is Ω² r directed outward, which I believe you will agree is no surprise. The discussion parallels very closely the discussion cited in Stommel and Moore. Brews ohare (talk) 05:21, 16 August 2008 (UTC)

Centrifugal force in general curvilinear coordinates (again)

Wolfkeeper: You do not seem to have read my comments upon this wording when it first appeared. There are defects that must be fixed. Whether or not you have taken the time to really look at it, this section contradicts some very basic facts, and is completely opposite to much of what is said in the Polar coordinate version, which is, after all, a special case of curvilinear coordinates. It also only appears to have citations, as many of the citations apply only to peripheral matters and do not document what is asserted in the sentence they are attached to.Brews ohare (talk) 16:03, 16 August 2008 (UTC)

This section has been completely rewritten and the relevant math included. An excellent exposition by Silberstein with a full view on google straightens out the entire mess. Brews ohare (talk) 15:41, 17 August 2008 (UTC)

Besides the text NOT being available on google books. (but elsewhere online), I am not sure that a text from the period (1922!) that the interpretation of GR was still under hot debate, and well before the proper definition of frame in GR (Weyl 1929) will really help resolve the issues. Since that text was written our understand and interpretation of what was really going on has increased dramatically. (TimothyRias (talk) 10:00, 18 August 2008 (UTC))

When I click on the link provided above (Silberstein), the book immediately opens. Of course, the general theory of relativity itself has evolved over time. Please indicate, however, how Silberstein's discussion of the issue at hand (lumping different types of forces together and calling them all by a single name: "fictitious forces") has "evolved". Notice that he treats the case of polar coordinates explicitly as an example of the general approach. Brews ohare (talk) 15:32, 18 August 2008 (UTC)

"State of motion" vs. "coordinates"? It is all about frames.

I find the difference being made made between "coordinate" and "state of motion" fictious forces being made in this article to be somewhat artificial. It seems to complete ignore the fact both just define a particular frame. (Or rather tetrad as the properly defined concept is called.) (TimothyRias (talk) 10:00, 18 August 2008 (UTC))

If your introduction of the term tetrad indicates an aim to provide a discussion valid for general relativity, please say so. I'd be happy to see such a thing, but in another article.

Your description of "artificial" distinctions is dealt with in more detail shortly. Brews ohare (talk) 16:22, 18 August 2008 (UTC)

The introduction of no-flat geometries in general relativity has forced us to reevalute what exactly we mean with frame since the old naive approach often figuring hypothetical physical realizations using rigid rods and clocks. It was realized that the proper way to fix a frame is to assign an "state-of-motion" and orientation to each event in spacetime. The mathematical way to describe such an assignment is a tetrad. (note that a state of motion is described by a single timelike vector and an orientation by three spacelike vectors, togehter they form an orientation in spacetime.) This concept in itself has nothing to do with GR, it is just the proper description of something which wasn't very rigidly defined in the past. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Hi Timothy: I have looked at the articles Frame fields in general relativity Dirac_equation#Curved_spacetime_Dirac_equation and Atlas (topology) in pursuit of more information about your remarks above. My reaction (please excuse me) is that this material should not affect this article on this basis:

1. It is (I'd say) too abstruse for simple exposition.
2. It is not used by the vast majority of textbooks or monographs, even at a graduate level. Which is to imply that the views I have expressed may be less profound, but are definitely more accessible and in common use throughout physics, engineering, robotics and meteorology.
3. A careful exposition of these ideas on Wikipedia requires several new pages to be written by an expert. The existing pages Frame fields in general relativity Dirac_equation#Curved_spacetime_Dirac_equation and Atlas (topology), while pertinent, are not oriented toward the discussion of fictitious forces, and their application to this topic is presently not developed.

Just what the implications of these topics may be for the topic of fictitious forces is unclear. I have no doubt that one can assign a tetrad, and a team of observers already has been suggested as more appropriate than a single observer at Observer (special relativity) and family of observers. I am not clear that this elaboration of the term "observer" has any direct impact on what has been said in the present article. We have your exposition above, but you have not shown its implications for the topic of fictitious forces. Are you interested in fleshing all this out with appropriate references and quotations in some kind of accessible language? Brews ohare (talk) 16:11, 19 August 2008 (UTC)

I'm not advocating talking about tetrads in this article. That would way too technical for the intended audience. The main point I'm arguing is that the article should not try so hard to explain the perceived difference between "state-of-motion" and "coordinate" fictitious forces. Especially since the last isn't anymore related too coordinates than the first. It is also related to the use of a different frame. But one that fails to be inertial in a slightly different way, then the first. I guess the main implication for this article is that you should not be making a fuss about such a subtle difference. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

First of all let me point out that "state of motion" alone is not enough to get centrifugal force even in a rotating frame, an orientation also needs to be specified. (An easy example of this is given by the origin in a rotating frame. Its state of motion is "stationary", centrifugal force is caused by the fact that the orientation of the origin is continuously changing (with respect to the orientation defined in an "inertial" frame). Specifying a "state of motion" and orientation at every point in space, is in fact specifying a tetrad.(TimothyRias (talk) 10:00, 18 August 2008 (UTC))

There is no statement that "state-of-motion" is "all that is needed". The statement is rather that "state-of-motion" is a factor deciding whether or not the fictitious force is zero in "state-of-motion" fictitious forces, while "coordinate" fictitious forces can be non-zero even in an inertial frame of reference. That is not an artificial difference. Brews ohare (talk) 15:23, 18 August 2008 (UTC)

A frame being inertial is not in any way fixed by the state-of-motion of any single observer. (again envision the observer at the center of a rotating frame, his state-of-motion is constant, yet the frame is not inertial.) It is determind by the state-of-motions and orientations of ALL events being "aligned". In traditional classical mechanics the alignment of the orientations was pretty much always assumed (implicitly exploiting the poincare symmetry of flat space and hence somewhat of a mathematical slight of hand), and kept in dependent of the choice of coordinates. Doing this in polar coordinates leads extra terms in the velocities and accelrations (as we all know well). Choosing to view these extra terms as fictitious forces is related to a certain choice of orientations which are not aligned, just as choosing to view the extra terms in a rotating frame as fictitious forces is related to the states-of-motion not being aligned. Both choices are a deviation from the inertial frame. The first one is just one that you (seem to be) are not familiar with. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Hi Timothy: Well again I'd say a team of observers already has been suggested as more appropriate than a single observer at Observer (special relativity) and family of observers. I am inclined to discount this notion that the whole idea of a connection between "inertial frame" and "state-of-motion" is disqualified because a single observer can't determine the meaning of the word "orientation" and needs a team of observers to do so. The observer in Newton's example of two tethered rotating spheres had no difficulty determining they were rotating, and not the fixed stars. And Newton's observer did not need a coordinate system, never mind a tetrad. Whatever the tetrad approach may bring to this problem, it has to result in pretty much the same picture. That means, among other things, that centrifugal force vanishes in inertial frames, in stark contrast to the "coordinate" version of centrifugal force, which is non-zero in inertial frames. Your definition of "observer" may be too narrow to encompass the classical observer, and replacing that observer by a team of observers has little consequence for the present article. Brews ohare (talk) 19:23, 19 August 2008 (UTC)

The thing is that you already need a team of observers to describe the states-of-motion in a rotating frame. We are however very much used to exploiting the flatness of space to generate such a family from the state-of-motion and orientation of a single observer. This method is very much embedded in the classical idea of a global frame as Newton was using. But even a global frame needs to specify its orientation. (although this is usually done implicitly as a hidden assumption.)

I'd also like to stress that consider the acceleration terms in polar coordinates is connected to attaching the coordinates to a non-inertial frame. Just like viewing the acceleration terms in a rotating coordinate system as ficitious forces is related to attaching them to a rotating frame. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

A practical manner of assigning a tetrad is by first defining a coordinate system, and then using the coordinates basis at each point to define the tetrad. (This approach is commonly taken in GR.) An other approach, frequently taken in classical mechanics, is to assign assign "states of motion" everywhere but orientations only at one point in space, and using parallel transport assisted by flatness of space to extend this orientation to the entirity of space. This approach leads to a choice of orientation that is independent of the choice of spacial coordinates. (TimothyRias (talk) 10:00, 18 August 2008 (UTC))

Depending on the problem being solved, of course a variety of methods may be "practical". How do your remarks relate to the quotation in the article, repeated below:

We first introduce the notion of reference frame, itself related to the idea of observer: the reference frame is, in some sense, the "Euclidean space carried by the observer". Let us give a more mathematical definition:… the reference frame is... the set of all points in the Euclidean space with the rigid body motion of the observer. The frame, denoted ${\mathfrak {R}}$, is said to move with the observer.… The spatial positions of particles are labelled relative to a frame ${\mathfrak {R}}$ by establishing a coordinate system R with origin O. The corresponding set of axes, sharing the rigid body motion of the frame ${\mathfrak {R}}$, can be considered to give a physical realization of ${\mathfrak {R}}$. In a frame ${\mathfrak {R}}$, coordinates are changed from R to R' by carrying out, at each instant of time, the same coordinate transformation on the components of intrinsic objects (vectors and tensors) introduced to represent physical quantities in this frame.

— Jean Salençon, Stephen Lyle. (2001). Handbook of Continuum Mechanics: General Concepts, Thermoelasticity p. 9

Please relate your remarks to the article at hand. Brews ohare (talk) 16:18, 18 August 2008 (UTC)

Well very simple with the terms "rigid body" the author is implying that he uses the translation spacial symmetry to extend the orientation of the observer to the entire spacial slice. He thus gives a limited definition of frame which suffices for his purpose. (much in the way that many mathematical authors will define functions to continuous, simply because at the present they do not wish to concider noncontinuous functions. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Timothy: Might not the present Wiki article on centrifugal force also be "limited" but "suffice for its purposes"? Brews ohare (talk) 19:03, 19 August 2008 (UTC)

I have very little problem with keeping the scope somewhat limited. My gripe is with the amount of weight being given to discerning between "coordinate" and "state-of-motion". (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

For polar coordinates these approaches lead to different choices of frame. Insisting that these frames are "straight" leads to the inclusion of fictious forces in the first while it does not in the second. Brews has systematicly tried to label this difference as purely mathemtical, while in fact it is the direct result of the very physical choice of frame. (well, at least just as physical as the choice between a rotating and an inertial frame.)(TimothyRias (talk) 10:00, 18 August 2008 (UTC))

You are using the term "frame" in your sense of the word, not in the sense used in the article and in the usual discussion of this topic. The standard meaning of frame refers to a state of motion of the observer, and leads to the distinction between inertial and non-inertial frames. Brews ohare (talk) 16:37, 18 August 2008 (UTC)

Again the state-of-motion of an observer is not sufficient to establish wether a frame is inertial. You will also need his orientation and a way of extending this to the rest of space. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Just how the extension from "observer" to a "family of observers" changes the exposition is unclear to me. The idea of "extending orientation to the rest of space" sounds a bit like the introduction of Christoffel symbols, and this approach is subject to the same issues about two types of fictitious force, as was discussed by Silberstein. Brews ohare (talk) 17:05, 19 August 2008 (UTC)

Using parallel transport (which is basically defined by the christoffel symbols) to extend the orienation to the rest of space, is one (very much geometry based) systematic approach to this extension. However any arbitrary choice of extension is, a priori, valid. It basically specifies how the observer would imagine his orientation (and state-of-motion) to be were he at the other position. The parallel transport approach is basically the one that is physically realized of you use as hypothetical system of rigid rods to define your frame of reference. You might even argue that such an approach is physically favoured. However the same arguments favour the same approach for extending the orientation and state-of-motion to extend it to the whole space time, leading to an inertial frame. Letting go of one, but not the other is a somewhat arbitrary choice made (sometimes unconsciencelessly) in many physics texts. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

Now, does this make the centrifugal force in a rotating frame and the one in the polar coordinate frame the same? Yes and No.(TimothyRias (talk) 10:00, 18 August 2008 (UTC))

This sentence misuses vocabulary: a rotating frame is a non-inertial frame and implies an observer accelerating relative to (say) the fixed stars. The term "polar coordinate" is a mathematical descriptor of a particular type of coordinate system, and is not in and of itself attached to any observer, and may be used in both inertial frames and non-inertial frames. In fact, exactly this is done in the article. Polar coordinates are used first in an inertial frame, and then in a rotating (non-inertial) frame, and then the two are compared. Brews ohare (talk) 16:37, 18 August 2008 (UTC)

As I have explained before polar coordinates can be used to define a non-inertial frame simply by picking the coordinate basis at each point as the orientation for that point. These orientations are not aligned hence the resulting frame is not inertial. It is not necesary to use this frame when using polar coordinates, but when doing so pretending that the orientations are in fact aligned leads to concidering the the extra acceleration terms as ficitious forces. Obviously with "polar coordinate frame" I mean the frame that can be naturally defined by polar coordinates. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Timothy: Apparently you have introduced a definition of "inertial frame" here in terms of the connection between the orientations adopted at different points in space time. Some more detail would be nice. How does this definition connect with the notion of "real" vs. "fictitious" forces? Some forces can be transformed away, and others cannot? And if your frame contains "fictitious forces" can it still be "inertial"? I suspect that you have in mind the formalism using Christoffel symbols. That is exactly the quagmire explored in the Silberstein citation provided in the article, and does not lead us away from the distinction between two types of "fictitious force". Brews ohare (talk) 18:46, 19 August 2008 (UTC)

In the (admittedly somewhat ad hoc) definition for inertial frame, no fictitious force would ever be present in an inertial frame. That is if we accept the convention that fictious forces are the force that are introduced by simply assuming that a reference frame is aligned. This is obviously somewhat of tautology, due to the definition of fictitious. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

Clearly they appear in different choices of frame, hence they are different. Yet, they arise as a result of the same physical reasoning (they are both fictious forces resulting from think of a "nonstraight" frame as "straight") and are both "outward pointing", making them very similar. With the difference and simularities being so subtle most textbooks choose the circumventing the issues (or just plain ignore it and just label both as "the" centrifugal force) adopting a "who cares where you put those acceleration terms, just put them somewhere and analyse the differential equations" additude.(TimothyRias (talk) 10:00, 18 August 2008 (UTC))

It is not a difference in choice of "frame" that is involved here. The subsection on polar coordinates shows that describing the movement of a particle in an inertial frame the equation for acceleration is:

${\frac {d^{2}\mathbf {r} }{dt^{2}}}={\boldsymbol {a}}=({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\mathbf {r} }}+(r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}){\hat {\boldsymbol {\theta }}}\ ,$

and is used directly in Newton's second law as:

${\boldsymbol {F}}=m{\boldsymbol {a}}\ ,$

where F is the real external net force. The frame is inertial so no fictitious force is recognized because this is simply Newton's law in polar form. The Stommel reference makes the very same point.

However, in the "coordinate" approach in this exact same inertial frame the term $-r{\dot {\theta }}^{2}$ is called a "fictitious force": same frame, different "fictitious forces"; one approach zero forces, the other approach non-zero forces even though the frame is inertial. Newton's law in the coordinate view becomes:

${\boldsymbol {F}}+mr{\dot {\theta }}^{2}{\hat {\mathbf {r} }}-2m{\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}=m{\boldsymbol {a}}\ ,$

with

${\boldsymbol {a}}=({\ddot {r}}){\hat {\mathbf {r} }}+(r{\ddot {\theta }}){\hat {\boldsymbol {\theta }}}\ ,$

That is, the "acceleration" in the "coordinate view" contains only the second-order time derivatives of the coordinates, and all the other polar contributions are taken as fictitious forces to the force-side of the equation, and are non-zero even in this inertial frame of reference. Brews ohare (talk) 16:04, 18 August 2008 (UTC)

You do realize that you can repeat this whole rant for a rotating frame, right? (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

This exposition is applied to a rotating frame in the article, and the two are compared. I don't see why this argument is a "rant": what do you object to here? Brews ohare (talk) 16:11, 19 August 2008 (UTC)

My objection is that you can do exactly the samething with a rotating coordinate system attached to an inertial frame. You get an expression of Newton's law in rotating coordinates. Sticking to this frame it is unnatural to move the extra terms to force side of the equation. Doing so (in some sense) implies moving to the rotating frame defined by the coordinates. In the same way choosing to view the extra accelaration terms in polar coordinates as ficitious forces implies moving to a different frame. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

These observations are sensible, but the actual practice as exemplified by (but not limited to) Stommel is to follow this unnatural procedure. As indicated below in my remarks to Fugal, that means the introduction of non-zero fictitious forces in an inertial frame of reference, a no-no in the standard discussion of inertial frames. The same approach is used extensively in the design of robotic manipulators, which follows your "throw everything into the pot, who cares about terminology, and solve the DE's" approach. I speculate that this attitude evolves from using a Lagrangian formulation that leads naturally to equations with only second-order time derivatives on one side of the equations. See R. Kelly, V. Santibáñez, Antonio Loría (2005). Control of robot manipulators in joint space. Springer. p. p. 72. ISBN 1852339942. {{cite book}}: |page= has extra text (help)CS1 maint: multiple names: authors list (link) and Shuzhi S. Ge, Tong Heng Lee, Christopher John Harris (1998). Adaptive Neural Network Control of Robotic Manipulators. World Scientific. p. p. 48. ISBN 981023452X. {{cite book}}: |page= has extra text (help)CS1 maint: multiple names: authors list (link)

Brews ohare (talk) 15:39, 20 August 2008 (UTC)

(As a side note: in Lagrangian formalism all terms end up on the side of the equation of motion. (i.e. you get something of the form PDE = 0) I think you are however right in suspecting that this leads to a who cares what we call the individual terms attitude, just solve the damn thing already.)

As a more to the point response. What I was saying was that you can in fact introduce rotating coordinates in a inertial frame. When this is done you get the acceleration terms that you call "state-of-motion" centrifugal force, however we are still in the inertial frame. Really interpreting these terms as actually fictitious forces however requires us to switch to the frame that is natural to the coordinates, a rotating frame. This switch is often done implicitly when changing coordinates. This seems to be what Marion and Thornton do in their book; they forgo the distinction between coordinate systems and reference frames and just assume the convention that changing coordinates automatically means changing frames to the corresponding coordinate frame.

And I stress again that the coordinate frame corresponding to polar coordinates is not inertial. The problem of having non-zero fictitious forces in an inertial frame only exists if you attach polar coordinates to an inertial frame (instead of their coordinate frame), but that problem also exists for rotating coordinates when attached to an inertial frame. (TimothyRias (talk) 09:31, 21 August 2008 (UTC))

Timothy: Thanks for the comments. Your observations about Marion and Thornton are illuminating, and the obliquity of these authors is the source (I believe) of all the fuss raised by Fugal and Paolo.dL. Brews ohare (talk) 13:54, 21 August 2008 (UTC)

What does this mean for the wikipedia article? I see two options:

• Both are treated in a single article centrifugal force and it is just noted that both are "outward pointing" fictious forces in a nonstandard choice of frame.
• Two article are created (centrifugal force (rotating frame) and centrifugal force (polar coordinates) and centrifugal force becomes a disamb. page linking to the two. (TimothyRias (talk) 10:00, 18 August 2008 (UTC))

A similar idea is at centrifugal force (disambiguation). You might wish to comment on its formulation on its talk page. Brews ohare (talk) 15:43, 18 August 2008 (UTC)

Some options that I think should be avoided:

• Extensive treatment of centrifugal force in polar coordinates. Physical equations of motion are really beyond the scope of that article. Polar coordinates find use an all sorts of (non physics related) situations. It might get a small mention there as an application, but it should not get much more.

I really wish that we can stop arguing so much about this. (TimothyRias (talk) 10:00, 18 August 2008 (UTC))

Please read the article with more attention to detail. Brews ohare (talk) 15:23, 18 August 2008 (UTC)

Please start being a little less condescending for somebody who clearly has a very limited understanding of the development of the concept of reference frame in the 20th century. I realy am starting to get the feeling that I'm communicating with a 19th century brickwall paradigm. (TimothyRias (talk) 09:17, 19 August 2008 (UTC))

Trying to explain my viewpoint is not condescension, but is, in fact, a compliment. My request that you read the article more closely is simply my reaction that some of your remarks are addressed in the article, and you didn't notice that. Were you to propose some change in wording, it would serve the purpose of telling me that you had actually read the material, eh?

I find your exposition about inertial frames and "state-of-motion" and orientation to each event in spacetime interesting, and would like to see you undertake a contribution to an article (maybe a new one) about this topic.

Somewhere above you say:

With the difference and similarities being so subtle most textbooks choose to circumvent the issues (or just plain ignore them and just label both as "the" centrifugal force) adopting a "who cares where you put those acceleration terms, just put them somewhere and analyze the differential equations" attitude.

This quote suggests you do think there is a "subtle" distinction between the two designations of fictitious force, and not simply no distinction. Is that so? Could you express this distinction from the tetrad viewpoint? Brews ohare (talk) 19:55, 19 August 2008 (UTC)

Well clearly there is some difference. Due to the fact that spacetime is pseudo riemanian a tetrad splits into a timelike vector field (which in this discussion has been refered to as the state-of-motion) and a triple of spacelike vectorfields (which we have called orientation). The so called "state-of-motion fictitious forces" are related to the timelike part of the tetrad not being "aligned", while the so called "coordinate ficititious forces" are related to the spacelike part of the tetrad not being aligned. Hence there is a minor distinction between the two and regarding them as different is somewhat inline with other ways that we treat time and space assymmetrically.

And because we treat time and space differently in many situations the two "types" of fictious forces may sometimes manifest differently. For example, due to the habit in classical mechanics of regarding time as an external absolute parameter, different choices for the spacelike part may always be connected to a choice of coordinates, making it seem that a simple coordinate transformation is all that is needed to transform the related fictitious forces away. (while it becomes impossible to do simple time dependent coordinate changes, and those get a somewhat special status.)

But in the end the distinction is a somewhat arbitrary one induced by our methods of discribing physics, while the connection between the two as actually quite physical. (TimothyRias (talk) 10:04, 20 August 2008 (UTC))

Suggestion for Resolution

It occurs to me that the current article would be just fine if only it was given the more accurate name "Brews Ohare's Personal POV and Commentary on Centrifugal Force and Other Miscellaneous Topics". If this were the article's title, there would be much less dispute over the content, since it would be, by definition, whatever Brews wants it to be (although it might then be more appropriately hosted somewhere other than Wikipedia). The current article is brimming over with neoligisms like "coordinate fictitious force" and "state-of-motion fictitious force", and elaborate attempts to rationalize Brews' personal (and evolving) ideas about what these newly minted terms ought to mean. From the standpoint of Wikipedia, this article has become truly pathological, bloated to the point of being unreadable. And whenever someone makes the slightest attempt to modify it, they are bombarded with ten or twenty counter-edits from Brews, coupled with an equal number of interminable rants on the discussion page, where we are informed that his beliefs are "beyond controversy". Several people have suggested (independently) that Brews should relinquish ownership and take a much needed break, but he shows no signs of taking this advice. The entire article has become a novel narrative interwoven with original research and highly POV rationalizations, all aimed at trying to justify why Brews' somewhat naive and unsophisticated view of the subject is superior to all other views. This kind of exercise in polemics really isn't appropriate for a Wikipedia article (in my opinion).Fugal (talk) 13:39, 20 August 2008 (UTC)

Hi Fugal: The issue that is troubling on this page is very simply put: there are two definitions in use for fictitious force. Because they both use the same term "fictitious force" it is hard to talk about the two meanings without distinguishing between them. Hence, the "neologisms" of coordinate fictitious force and state-of-motion fictitious force. I am not tied to these terms: do you think type A fictitious force and type B fictitious force would be more suitable?

A controversy arises whether there are in fact two different meanings. On this subject Timothy is of the mind that there is a difference, but it so subtle that it requires recognition of our prejudices about space-time differentiation and would require a five-year doctorate in general relativity and differential geometry to understand the distinction between the meanings. Therefore, the distinction is not worth bringing up, and we would be advised to ignore the difference and just label both as "the" centrifugal force, adopting a "who cares where you put those acceleration terms, just put them somewhere and analyze the differential equations" attitude.

My response to this view is very, very simple: one definition leads to fictitious forces that vanish in an inertial frame of reference; the other definition leads to forces that do not vanish in an inertial frame of reference. I do not find that to be subtle difference at all. For the case of polar coordinates, explicit mathematical forms for the forces in the two cases are presented that show exactly how the difference in the two definitions leads to two different sets of mathematical terms.

To spell this remark out as it is stated in the article, in an inertial frame of reference the force is simply the net real force F on a moving particle, and the "state-of-motion" fictitious force is zero regardless of the choice of coordinate system. The force in the "coordinate" view is:Stommel

${\boldsymbol {F}}+mr{\dot {\theta }}^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}\ ,$

in which F is the real net force just mentioned, and the other terms are the "coordinate" fictitious forces, which have a form that varies depending upon which type of curvilinear coordinates you want to use. Obviously, as this is an inertial frame, these extra "coordinate" fictitious forces are not only "fictitious", they also do not vanish in an inertial frame of reference, which is contrary to all discussions in the literature about inertial frames of reference and their relation to fictitious forces.

These are not subtleties; they are real differences that cannot be ducked.

Where do you weigh in on this? Brews ohare (talk) 14:34, 20 August 2008 (UTC)

I repeat:

1. Polar coordinates naturally attach to an non-inertial frame.
2. You can introduce a rotating coordinate system in any inertial frame. Doing so will lead to additional acceleration terms, which may be interpreted as fictitious forces (although such an interpretation is unnatural without changing frames) and which are non-zero in the inertial frame. (TimothyRias (talk) 09:38, 21 August 2008 (UTC))

Hi Timothy: So, from these remarks I take it that you agree entirely with these latest comments of mine, and find them unsurprising? You might (I'm guessing) simply add that this approach is either (i) unnatural because it is not accompanied by a switch of frame as well as adoption of polar coordinates or (ii) implicitly anticipates such a switch but, unfortunately, often does not point out such anticipation. Brews ohare (talk) 13:37, 21 August 2008 (UTC)

(I'm not sure which latest remarks you are refering to, but I certainly disagree with "they are real differences that cannot be ducked" as the issue you raised exists for both "types" of centrifugal.) Yes, you could add that and (ii) is one of the things I have been trying to point out. (TimothyRias (talk) 14:56, 21 August 2008 (UTC))

Let me try again. You say:

which may be interpreted as fictitious forces (although such an interpretation is unnatural without changing frames) and which are non-zero in the inertial frame

which I take as not in conflict with my statement:

Obviously, as this is an inertial frame, these extra "coordinate" fictitious forces are not only "fictitious", they also do not vanish in an inertial frame of reference, which is contrary to all discussions in the literature about inertial frames of reference and their relation to fictitious forces.

Your remark:

the issue you raised exists for both "types" of centrifugal

is unclear to me. I will elaborate next on the two different uses of the term "fictitious force".

The "state-of-motion" centrifugal force is zero in an inertial frame of reference (by definition of an inertial frame), regardless of whether the coordinate system is Cartesian or curvilinear, as is stated in the article. To elaborate: in the inertial frame, Newtons' law in polar form is:

${\boldsymbol {F}}=m{\boldsymbol {a}}=m({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\mathbf {r} }}+m(r{\ddot {\theta }}+2{\dot {r}}\ ,$

and the force on the left is the real net force. The terms on the right are not interpreted as fictitious in the "state-of-motion" viewpoint, but simply as artifacts of the curvilinear coordinate system. Bluntly put, in the "state-of-motion" viewpoint, all fictitious forces are zero by definition of an inertial frame of reference. There simply are no fictitious forces in an inertial frame. I believe this viewpoint to be very basic to the connection between inertial frames and fictitious forces, as expressed, for example, by V. I. Arnol'd (1989). Mathematical Methods of Classical Mechanics. Springer. p. p. 129. ISBN 978-0-387-96890-2. {{cite book}}: |page= has extra text (help)

The equations of motion in an non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.

— V. I. Arnol'd: Mathematical Methods of Classical Mechanics Second Edition, p. 129

A slightly different tack on the subject is: Iro

An additional force due to nonuniform relative motion of two reference frames is called a pseudo-force.

— H Iro in A Modern Approach to Classical Mechanics p. 180

It seems clear to me that terms introduced not by relative motion, but by change in coordinate system (say from Cartesian to polar coordinates in the same frame of reference, same origin, same state of motion) do not qualify as "pseudo-forces".

That viewpoint is different from the "coordinate viewpoint", where Newton's law (still in an inertial frame of reference) is rearranged to put some terms on the force-side: see Stommel

${\boldsymbol {F}}+mr{\dot {\theta }}^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}=m{\tilde {\boldsymbol {a}}}=m{\ddot {r}}{\hat {\mathbf {r} }}+mr{\ddot {\theta }}{\hat {\boldsymbol {\theta }}}\ ,$

where a "coordinate" version of the "acceleration" is introduced:

${\tilde {\boldsymbol {a}}}={\ddot {r}}{\hat {\mathbf {r} }}+r{\ddot {\theta }}{\hat {\boldsymbol {\theta }}}\ ,$

consisting of only second-order time derivatives of the coordinates r and θ. A "coordinate" fictitious force is thereby introduced:

${\boldsymbol {F_{fict}}}=mr{\dot {\theta }}^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}\ ,$

that is non-zero in the inertial frame.

Do you have any issues with this formulation of the difference between the two uses of the term "fictitious force"?

Parenthetically I would add that this problem does not go away by changing terms from "fictitious" to "apparent" or to "pseudo", because the ambiguity extends to two uses of the terms "centrifugal" and Coriolis". Brews ohare (talk) 18:27, 21 August 2008 (UTC)

Suggestion for Resolution(Cont'd)

A fictitious force derived in an inertial frame implies switch to non-inertial frame

Comment by TimothyRias:

You seem to have missed my point:

Let's do it a bit more explicitly. Suppose we have an inertial frame with cartesian coordinates x and y. (for convenience we drop de third coordinates). In this frame we can adopt new (time dependent) coordinates: (disclaimer any equations should be read module missing/extra signs)

$X=\cos(wt)x+\sin(wt)y\;$

$Y=\cos(wt)y-\sin(wt)x\;$

If we do so we get the following acceleration:

${\vec {a}}=({\ddot {X}}-2w{\dot {Y}}-w^{2}X){\hat {X}}+({\ddot {Y}}+2w{\dot {X}}-w^{2}Y){\hat {Y}}$

We can introduce a "coordinate acceleration"

${\tilde {\vec {a}}}={\ddot {X}}{\hat {X}}+{\ddot {Y}}{\hat {Y}}$

By which we introduce a coordinate fictitious force:

${\vec {F}}_{fict}=(2w{\dot {Y}}+w^{2}X){\hat {X}}+(-2w{\dot {X}}+w^{2}:Y){\hat {Y}}$

You will recognize these as the regular expressions for the fictitious forces in a rotating frame. However we are still an inertial frame, hence by definition (of fictitious force) these cannot be fictitious forces. Interpreting these as fictitious forces implies going to the corresponding rotating frame; the coordinate frame of the choosen coordinates. This is quite general, interpreting the extra acceleration terms in certain coordinates as fictitious forces always implies adopting the coordinate frame. When these extra terms are non-zero it also implies that the coordinate frame in non-inertial. The polar coordinate frame fictitious forces being non-zero when applying the coordinates to an inertial frame doesn't make them different from the rotating frame fictitious forces. The rotating frame fictitious are also non-zero if you apply the corresponding coordinates to an inertial frame. Hence the thing that you described above as a real difference that cant be ducked is a not difference at all. It is just a difference in the way you have been treating the two cases, but each treatment can be applied to both cases. (TimothyRias (talk) 09:09, 22 August 2008 (UTC))

Thanks much for becoming specific. I now understand what you are saying. From this perspective, I'd add the following remarks:

1. Unless one adopts your view that calling certain acceleration terms in an inertial frame "fictitious" definitely implies ipso facto that a change of frame to a non-inertial frame is made, the idea that these terms are fictitious forces in the common meaning of that term (as per the quotations above from Arnol'd and Iro) is nonsense.

Yes, this is true both for the acceleration terms in rotating coordinates as those in polar coordinates. You might even turn it around. The definitions of fictitious force given by Arnol'd and Iro imply that calling anything a fictitious force must imply adopting some non-inertial frame. (TimothyRias (talk) 10:31, 25 August 2008 (UTC))

Glad we agree on this point. Brews ohare (talk) 16:03, 25 August 2008 (UTC)

2. If a change to a non-inertial frame is implied, one must face the prospect that there are an infinity of non-inertial frames, and one must choose which one is implied . Thus, mere implication of the switch of frames is very ambiguous. It would be pertinent to specify which frame is implied.

Not so ambigious actually. The implied change is toward the coordinate frame of the chosen coordinates. This convention for defining your frame is commonly adopted in GR, because it is by far the easiest way to specify a frame in a more general context. (TimothyRias (talk) 10:31, 25 August 2008 (UTC))

Point to be clarified. A switch to polar coordinates is not in itself unique. For example, is it a switch to a rotating set of polar coordinates? If so, at what rate does it rotate. what is its Ω? Clearly, the centrifugal force depends upon Ω and cannot be specified without it. Taylor Classical Mechanics p. 358 suggests the co-rotating frame, by which is meant a frame selected at a specific time t to have the rate of rotation of the observed particle Ω = dθ/dt at that moment. In this instantaneous frame that must be reselected at every moment, he suggests easy identification of terms at that moment is possible. I added this to Polar_coordinate_system#Centrifugal_and_Coriolis_terms and removed your . Brews ohare (talk) 00:36, 26 August 2008 (UTC)

I would not normally call rotating polar coordinates, "polar coordinates", I would instead just call them "rotating polar coordinates". It is also clear that "rotating polar coordinates" and normal "polar coordinates" imply different frames.(TimothyRias (talk) 09:54, 27 August 2008 (UTC))

No problem with this; do you think I have said differently? Brews ohare (talk) 19:54, 27 August 2008 (UTC)

Once a particular set of coordinates is chosen, this identifies a unique adapted frame.(TimothyRias (talk) 09:54, 27 August 2008 (UTC))

No agreement here; the frame refers to e.g. inertial or non-inertial, not to coordinate system. Brews ohare (talk) 19:54, 27 August 2008 (UTC)

Simply take the coordinate base as the tetrad. (Note this only works directly for coordinate systems in which the coordinate base is already orthonormal such a Cartesian or polar coordinates. For more general coordinates a more advanced recipe may be required orthonormalizing the base.) (TimothyRias (talk) 09:54, 27 August 2008 (UTC))

You say :I would not normally call rotating polar coordinates, "polar coordinates", I would instead just call them "rotating polar coordinates". What? I have been very careful to distinguish between polar coordinates in inertial and in non-inertial frames. Your notion that the coordinate system implies a frame is incorrect: a frame can be chosen and then a variety of choices is available for coordinate system. The reverse order of events is not germane here. Brews ohare (talk) 15:38, 27 August 2008 (UTC)

Of course, you can use any set of coordinates with any frame, the two are, a priori, independent concepts. We both agree on this, so I tier from having you imply that I imply otherwise. (I suggest that you aren't even trying to understand what I'm saying here.) This works both ways, you can first select coordinates and then a frame of visa versa. There is however a well known procedure for obtaining a choice of frame from a choice of coordinates (see for example Norton): (In the definition of frame used by Norton:) take the congruence of timelike curves defined by constant spacelike coordinates as your frame. Note that in this definition, indeed polar and cartesian coordinates yield the same choice of frame. Taking the slightly more general definition of frame that also includes a specification of the orientation of at each event, then these two coordinate systems will yield different frames. Easy. (TimothyRias (talk) 16:26, 27 August 2008 (UTC))

Hi Timothy. How about sticking to the context of classical mechanics? Or do you really want to write a whole subsection on tetrads and fictitious forces using a "congruence of time-like curves"?? After that you could connect this digression back to the topic of this article based upon classical mechanics. I'd prefer to settle the issues in the classical setting first, and then digress. Brews ohare (talk) 19:54, 27 August 2008 (UTC)

3. If switching is implied, the variables must be redefined by implication as well. For example, using the fictitious force ${\boldsymbol {F_{fict}}}=mr{\dot {\theta }}^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}{\hat {\boldsymbol {\theta }}}\ ,$, the original meaning of the variables r, θ refer to the position of a moving particle, and are only indirectly related to the rotation Ω of any frame of reference (because the particle is moving in some curved path, it has its own angular velocity in any frame). This point is noted by Stommel, for example, who distinguishes between Ω and the full angular velocity of the particle dθ/dt .

Actually this is not necessary. This change was done by the change of coordinates already. Adopting the corresponding coordinate frame just makes it easier to interpret the coordinate values. (TimothyRias (talk) 10:31, 25 August 2008 (UTC))

I don't follow you here: if the polar coordinate values r and θ are the coordinates of the particle observed in polar coordinates in the inertial frame, a particular rotating frame must be selected before the corresponding variables r' and θ' in that frame can be set up. That is, one must select a particular rotating frame before one can proceed. Are we talking about the same thing here? Brews ohare (talk) 16:03, 25 August 2008 (UTC)

We don't need a rotating frame in polar coordinate case. We need a frame in which the orientation is dependent on the (spacial) position. Specifically, we need the frame to which polar coordinates are adapted namely the one in which the orientation is always aligned with the radial direction (and the state-of-motion does not vary with time or space). Changing to this frame does not change the coordinate expressions in polar coordinates, it merely changes their interpretation. (Just like adapting a rotating frame when already using rotating coordinates, just changes the interpretation of the coordinates and coordinate expressions.) (TimothyRias (talk) 09:54, 27 August 2008 (UTC))

The connection between "frame" and "orientation" is lacking in a classical framework: one can choose a Cartesian coordinate system in a chosen frame with any orientation. As another example, a polar coordinate system (classically) has orientation only for the z-direction. I'd suggest that if a "deeper" concept of orientation based upon differential geometry in a general relativistic framework is necessary to understanding "orientation" that at a minimum it is necessary to make a separate subsection to develop the notion, and that most probably it should not be part of this article at all. And I am unclear that there is any bearing at all upon what is being discussed. Brews ohare (talk) 15:33, 27 August 2008 (UTC)

4. No author that I can find has said either that a frame change is implied, or provided any guidance as to just what frame and what variable changes might be implied.

You might wanna check your old pal Norton on this. He clearly mentions the convetnion of letting the frame be specified by the coordinates. (TimothyRias (talk) 10:31, 25 August 2008 (UTC))

Norton mentions this "convention" (p. 836) only as a position that he does not agree with and that has problems associated with it (particularly in rotating frames) that are the subject of a long discussion in his paper. Following his introduction of this viewpoint he says (p. 837) "More recently, to negotiate the obvious ambiguities of Einstein’s treatment, the notion of frame of reference has reappeared as a structure distinct from a coordinate system."

Additional citations by many different authors supporting the distinction between frames of reference and coordinate systems are found in frame of reference. Brews ohare (talk) 16:55, 25 August 2008 (UTC)

Sigh, did I say they were the same? No, I didn't, did I? What I said was that a particular coordinate system can be used to define a frame of reference. This specifically alluded to be Norton when discussing the alternative version of the definition of a frame using equivalence classes of coordinate systems adapted to some congruence of curves. (As a small aside: not all coordinate systems will allow this, at least in Norton's sense, since not all coordinate systems will have clear timelike and spacelike coordinates. Take an form of lightcone coordinates, which do not have any timelike coordinates, but instead of two lightlike coordinates.) He also mentions the convention in GR of always assuming the frame corresponding to the coordinates. What he critizes is the notion that this convention implies that er is no difference between the two concepts.

Sigh away; If there is a deeper meaning here, instead of sighing, you might try explanation. And there is a distinction between "can be used" and "must be used". You have a lot of technical blah-blah here that seems beyond the scope of the article and only vaguely related to the issues at hand. Brews ohare (talk) 15:33, 27 August 2008 (UTC)

On the same page, he also mentions that in the definition of frame that he will be using the properties of the metric to identify changes of rotation (i.e. he uses paralell transport to assign orientations to each timelike curve.) He also mentions that you can have a more general definition of frame by adding a continous specification of the orientation to curves (or rather a spacelike triad to the timelike vectorfield to form a tetrad). It is this more general definition of frame that I have been referring to as needed to make physical sense of the centrifugal force in polar coordinates. (TimothyRias (talk) 09:36, 27 August 2008 (UTC))

And the implication and conclusion is? Can you package these observations of yours in some way meaningful to the article? The objective here is to relate two approaches to finding "fictitious forces", which may sometimes agree, but as commonly used, often do not. Brews ohare (talk) 12:52, 28 August 2008 (UTC)

Perhaps support by reference to a source can be found for the idea that frame change is implied by adoption of the words "fictional force"?

Supposing that can be done, the article could be modified to say:

"Sometimes authors intend the use of "fictional force" in the "coordinate" sense to imply ipso facto a change of frame to a non-inertial frame where these forces are in fact "fictitious forces" in the sense of standard classical mechanics. For example , see authors A, B, C, who indicate that the correct way to introduce "fictitious forces" by implication is to follow the recipe below to insure a correct choice of non-inertial frame (among the infinity of possible such frames) where in fact these particular terms become the correct fictitious forces."

If sources to cite cannot be found, an alternative revision is based upon finding a recipe that leads to versions of "coordinate" fictional forces that are the same as the "state-of-motion" fictional forces. To set up some such revision, take the example of the rotating frame in the article where the "coordinate" fictitious force is:

${\boldsymbol {F_{fict}}}=mr{\dot {\theta }}'^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}'{\hat {\boldsymbol {\theta }}}+m\left(2r\Omega {\dot {\theta }}'+r\Omega ^{2}\right){\hat {\mathbf {r} }}-m\left(2{\dot {r}}\Omega \right){\hat {\boldsymbol {\theta }}}$

The first two terms are contributed by motion of the particle as seen in the rotating frame, and are the terms seen even when Ω = 0. The last two terms are the fictitious forces of classical mechanics. Thus, a possible recipe for determining fictitious forces is to write out Newton's laws in the inertial frame for a particular case of a particle motion, namely, in this case, one where $mr{\dot {\theta }}'^{2}{\hat {\mathbf {r} }}-m2{\dot {r}}{\dot {\theta }}'{\hat {\boldsymbol {\theta }}}=0$. For example, if one picks a particle that will be seen as stationary in the inertial frame one wishes to switch to, the correct centrifugal force will result (but the Coriolis force requires something else). Can it be done? Basically, one needs to calculate the trajectory of a particle in the selected non-inertial frame that is (apparently) in free motion, and use that trajectory in the inertial frame when finding the forces. That's a guess.

Assuming the recipe can be found, a possible revision would then be:

"It is possible to use the "coordinate" fictional forces approach in a manner that leads to the same "fictional forces" as the "state-of-motion" fictional forces. Here is the recipe: blah -blah -blah. Although this careful use of the "coordinate" fictional forces approach leads to the same fictional forces as those of standard classical mechanics, it must be recognized that the literature often does not follow the above recipe. Consequently, versions of "coordinate" fictitious forces frequently are derived that violate the above prescription, and therefore are not "fictitious forces" in the "state-of-motion" sense in any frame of reference."

The objective here is to relate two approaches to finding "fictitious forces", which may sometimes agree, but as commonly used, often do not. Brews ohare (talk) 18:53, 22 August 2008 (UTC)

Fugal's commentary

The current article is getting filled up with attempts to rationalize the personal POV of one editor. It appears to me (although I haven't taken a formal vote) that the majority of other editors believe the neoligisms and novel narratives being woven by that editor are not reflective of any published reputable source. To some extent, this is probably unavoidable, because the topic in dispute is not considered to be significant enough (or difficult enough) to warrant being discussed explicitly in very many reputable sources. Most scientists understand what Christoffel symbols mean, and the fact that none of them are "more physical" than the others, but they don't feel it necessary to make a point of this obvious fact.

Maybe the best way forward is to move the last half of this article, beginning with the discussion of polar coordinates, to its own article, which could be on the general subject of centrifugal force, allowing this article to be focused just on Brewsian centrifugal force in rotating coordinates. I seem to recall that Brews said not long ago that he advocated moving this "insignificant side topic" to its own article, where he felt certain it would languish for lack of interest. If I remember rightly, he said once it was move from his page, he didn't care what happenned to it. So he is presumably all in favor of my proposal.Fugal (talk) 01:36, 24 August 2008 (UTC)

Hi Fugal: Everything in the article is well documented, while your comments and views are not. Earlier attempts to engage you in a documented discussion have been ignored by you: for example, here. So you now are simply stating your POV with far less justification than the views in the article. You claim the article says "some Christoffel symbols are more physical than others", which may be only sloppy reading of the article or may be poor polemic. Perhaps, instead of vague slaps at your undefined notion of a "Brewsian centrifugal force", you might attempt to provide valid, detailed, specific criticism backed up with real citations? In other words, perhaps you could be constructive? Brews ohare (talk) 16:27, 24 August 2008 (UTC)

A clear, complete, and concise explanation, fully supported by references from high quality published sources, was added to the article, and you summarily deleted it, and proceeded to replace it with your own novel narrative, which consists of whole sections without a single reference, in which neoligisms and novel notions and original research are introduced. And now YOU ask ME to be constructive and provide real citations? Sheesh. Look, your original research about "state of motion fictitious forces" and "coordinate fictitious forces" simply does not belong in Wikipedia. You know very well it is original research, and every other editor here knows it is original research. If you really want me to be constructive, I'll be happy to go in and delete all your original research and novel narrative and replace it with well-sourced and accurate material. Is this what you are asking me to do?

I also note that you declined to comment on my proposal above, which is that, now that this article is specifically about rotating coordinates, the other material discussing the more general view really belongs in another article, devoted to the general topic of centrifugal force and other fictitious forces. This material certainly doesn't belong here in this rotating frames article. Fugal (talk) 18:49, 24 August 2008 (UTC)

I really don't care about the curvilinear section with Christoffel symbols: it is there because Wolfkeeper asked for such a section.

The section on polar coordinates is about a comparison between polar coordinates in rotating and in inertial frames. So it reasonably belongs here. It is somewhat lengthy in order to present clearly that "ficititous force", in particular centrifugal and Coriolis force, are used in two different meanings. These two meanings crop up most obviously in polar coordinates, although they also arise in the use of curvilinear coordinates. I think you do not subscribe to the idea of two meanings, but it is far from original research. Citations are provided where the use of "ficitious forces" is suggested in inertial frames, in clear contradiction to the quotations from Arnol'd and Iro you can find higher on this page. This contradiction can be viewed (most reasonably) as two uses of the same term or, if you prefer, a misuse of the terminology by a large number of writers (not my choice for description). You are attached to one meaning at the exclusion of the other, or possibly wish to conflate the two meanings. Brews ohare (talk) 20:17, 24 August 2008 (UTC)

It isn't for Wikipedia editors to pass judgement on whether published reputable sources are "mis-using" terminology, we are just to accurately represent what those sources say. What we have here is one set of introductory texts that give a simplified and restricted view of the subject, and then several advanced grown-up references that give a more general and comprehensive view of the subject, so both deserve to be accurately represented (per Wikipedia policy), although most editors would tend to lean toward the more general and comprehensive view..Fugal (talk) 21:04, 24 August 2008 (UTC)

The idea that there is a simplisitic and a more general view is undocumented. Also, you have not stated just what exactly is the general view, nor cited sources, nor provided any quotes. Brews ohare (talk) 21:20, 24 August 2008 (UTC)

In this situation there are multiple sources that seem superficially to say contradictory things, but as has been explained to you previously, they are contradictory only if you insist on imposing the Brewsian myopia onto them, and have only a sophomoric level of understanding of physics. Introductory texts tend to give a simplistic description of things, and unfortunately some students become embittered later when they learn, upon discovering more advanced material, that they were given a simplified view earlier in their education. They feel betrayed. Well, that's understandable, but we're not here to debate the merits of various pedigogical strategies in our educational system, we're here to present a topic accurately on the basis of the best available sources..Fugal (talk) 21:04, 24 August 2008 (UTC)

Well, you are very unkind to me. And do not document anything you say. Brews ohare (talk) 21:20, 24 August 2008 (UTC)

You mentioned the "most reasonable" interpretation is that terms are being used with different meanings, which to some extent is true, but one is just an informal and simplified version of the other. You seem to be intent on enshrining the simplistic 4th grade version as some kind of dignified and preferred "alternative" to the grown-up complete and treatments of the subject, and you seem to be intent on denigrating the latter. This is just motivated by your personal POV (in my opinion)..Fugal (talk) 21:04, 24 August 2008 (UTC)

That is exactly what it is: Your undocumented opinion. Brews ohare (talk) 21:20, 24 August 2008 (UTC)

I suspect it's all because you were given, by well-meaning teachers and text book writers in 4th grade, an overly simplified explanation of dynamics. The problem is, very few 4th grade students are prepared to absorb a treatise on the epistemology of scientific knowledge, so they are taught in terms of intuitive notions, despite the fact that those notions are ultimately untenable. The irony here is that you're intent on perpetuating the very over-simplification that was perpetrated on you.Fugal (talk) 21:04, 24 August 2008 (UTC)

Your fourth-grade education was more advanced than mine. However, you still have no documentation for your "grown-up" interpretations.

Look, we have very clear quotes from Arnol'd (an impeccable authority on the subject at a very sophisticated level) and Iro (a textbook, author's rep unknown to me, but a very standard statement) that fictitious forces do not arise in inertial frames. I do not see you challenging these authors. On the other hand, there are very clear quotes showing that some authors have defined fictitious forces so they do exist in inertial frames. What is there to argue about? Cited sources have used different meanings for the same terminology. All we can do is recognize the fact and point it out to the reader.

Timothy has suggested that using differential geometry in general relativity a somewhat more unifying approach can be found (just how unifying, or just how it is accomplished is unclear and undocumented). That idea is (i) unsupported so far by citation or quotation (ii) very advanced and beyond the average reader, and (iii) must reduce within the less heady atmosphere of classical mechanics to the same inglorious result of two different meanings. Brews ohare (talk) 21:39, 24 August 2008 (UTC)

You continue to say that no explanation or documentation for the grown-up unified version has been given, but that is not true. As stated above, a clear, complete, concise, and fully sourced explanation was added to the article, only to be deleted within hours by Brews ohare, replaced with his POV novel narrative and original research. You should read what you deleted, and pay particular attention to the definition of an inertial coordinate system. You may also need to work on your understanding of how coordinate systems are related to "frames", and challenge yourself to understand the difference between a frame and an observational frame.Fugal (talk) 01:03, 25 August 2008 (UTC)

I don't agree that a "clear, complete, concise, fully sourced explanation" was given. I don't agree that my understanding is limited in the ways you suggest. And I do not find anything that is germane to contradictory quotes indicating different usages of the same terms. Brews ohare (talk) 05:31, 25 August 2008 (UTC)

Anyone who cares to check the history of the article can see plainly that you're wrong. If you had read what was written, instead of simply deleteing it, you would have learned something. For example, you would understand that what seems to be contradictory usages of the same terms are really the same usage. But this would require you to read and comprehend, neither of which you seem inclined to do.

I repeat, the current article contains, in the sections beginning with polar coordinates, neoligisms and novel narrative and original research which is not appropriate for Wikipedia. The thesis that there are "state-of-motion fictitious forces" and "coordinate fictitious forces" is the fabrication of just a single editor here, as is all the nonsense about "attaching coordinate systems to frames", and none of this original research belongs in Wikipedia. This material is not verifiable from any reputable source, and should be removed.

The editor who inserted this material opposes its removal (surprise), and shows every sign that he intends to continue opposing its removal, but it nevertheless needs to be removed, per Wikipedia policy. These policies were specifically designed to restrain the contributions of individuals like this. The policies against original research and novel narratives need to be upheld.Fugal (talk) 05:57, 25 August 2008 (UTC)

You seem unwilling to say anything concrete or contributory and are simply focussed upon being nasty. State your case that I am "wrong" and provide your citations. Where material is not readily available on-line, add some quotations from the sources. Brews ohare (talk) 14:37, 25 August 2008 (UTC)

You're mistaken. I provided a perfectly concrete and contributory explanation, with reference, and you deleted it within 60 minutes of its appearance, and since then you've denied that I ever provided it. I repeat, you should go and read what you deleted. It answers all your questions, and clears up all your confusions.Fugal (talk) 17:27, 25 August 2008 (UTC)

Perhaps you refer to your Revision as of 21:30, 15 August 2008? It was removed with extensive comments at Reasons for removal to which no response was received. In addition, many of the issues already were presented at Fugal's positions, so far ignored by you.

Initially, you took the view that of course fictitious forces were non-zero in inertial frames: frames had nothing to do with it. That view is accurate for the "coordinate" terminology, but contradicts the meaning of an "inertial" frame in the sense of standard classical mechanics (above quotes from Arnol'd and Iro). So, let's relax and just look at the statement of the issue as given below. I don't think you really object to it. Brews ohare (talk) 05:31, 26 August 2008 (UTC)

Simple statement of the issue

Clear quotes from Arnol'd (an impeccable authority on the subject at a very sophisticated level) and Iro (a textbook, author's rep unknown to me, but a very standard statement) state that fictitious forces do not arise in inertial frames. No-one challenges these authors. On the other hand, there are very clear quotes showing that some authors have defined fictitious forces so they do exist in inertial frames. Among them are many in the area of design of robotic manipulators (for example, Ge et al. and Teshnehlab & Watanabe) and some standard works as well. Stommel, Shankar, and McQuarrie for example. What is there to argue about? Cited sources have used different meanings for the same terminology. All we can do is recognize the fact and point it out to the reader.

It seems to me that it is impossible to dispute the above facts. If dispute is attempted, it must show that in fact authors do not define fictitious forces that are non-zero in an inertial frame. Obviously, examples of this activity are already cited and cannot be made to go away. Brews ohare (talk) 17:46, 25 August 2008 (UTC)

The problem is that you fail to grasp the different contexts in which various texts make various statements. Understanding context is essential to a meaningful and accurate understanding of the literature... and this applies to the literature on any subject. Failure to understand the context can easily lead one to believe that authors are saying contradictory things, when in fact they are just stipulating different things and taking normal linguistic shortcuts for the purposes of their own discussions.

Let me give a concrete example from a reference source that is easily accessible to all: Einstein’s 1905 paper on special relativity. This paper talks a lot about coordinate systems and frames, but notice that at the beginning of section 3 the author introduces them by saying “Let us in stationary space take two systems of coordinates, i.e., two systems, each of three rigid material lines, perpendicular to each other and issuing from a point.” Note that he says “i.e.,” meaning “that is”, and not “e.g.” meaning “for example”. He is stipulating that hereafter when he says “coordinate system” in this context he means a rectilinear system of coordinates.Fugal (talk) 00:06, 29 August 2008 (UTC)

At this point, certain editors here may enter a state of panic, because they know full well that other reputable sources discuss “coordinate systems” that are not restricted to being rectilinear Cartesian coordinates, so we have two inconsistent usages!! Oh my God, what will we do??!! Does this mean we need two separate articles on coordinate systems, one devoted to the views of people who focus on rectilinear Cartesian systems, and another devoted to the “insignificant side topic” of people who "erroneously mis-use" the term “coordinate system” to refer to more general things like polar coordinates? After all, this isn’t a dictionary, it’s an encyclopedia. Just one definition per article. Blah Blah Blah.Fugal (talk) 00:06, 29 August 2008 (UTC)

Of course not. There’s no “inconsistency” here. No one supposes that Einstein would have disputed the existence of coordinate systems that do not conform to the attributes of the systems he described, and which he chose to call “coordinate systems”. He was simply defining the term for purposes of his discussion, and making certain stipulations to avoid dealing with issues that arise when discussing coordinate systems in full generality, since those issues were not the focus of his concern. It would be a gross misrepresentation to assert, on the basis of that paper, that Einstein advocated a restricted definition of the term "coordinate system", and it would be an even worse misrepresentation to assert that he believed all his subsequent statement, predicated on the noted stipulation, must apply in general. But this is precisely how a certain editor here is interpreting all the cited references.Fugal (talk) 00:06, 29 August 2008 (UTC)

It should be noted that another common way of stipulating the restricted view is to talk in terms of “frames”, which are just equivalence classes of mutually stationary coordinate systems, so they “mod out” any differences in the spatial coordinates. This applies to many texts on classical dynamics, where there is a (often tacit) stipulation that unless specifically noted to the contrary, the “default” coordinate system is rectilinear and Cartesian. Introductory books often make statements that are true within the limited context that they have described for the student, but that are not true in a more general context. Not all of those texts are careful enough to explicitly define the context (as Einstein did), but it would be silly to conclude that they dispute the existence of other kinds of coordinate systems. Nor are we entitled to infer from their failure to discuss the more general coordinate systems what they would say about them if they had chosen to discuss them. (Some students, upon discovering that they were taught simplified versions sometimes become embittered, and even turn into physics crackpots.)Fugal (talk) 00:06, 29 August 2008 (UTC)

Naturally if we stipulate that our statements about coordinate systems assume spatially rectilinear coordinates, or if we talk in terms of “frames”, thereby stipulating that we are choosing to "abstract away" any differences in spatial coordinates, then we can say without further ado that extra acceleration terms appear only in accelerating coordinate systems (or frames). But if we consider more general coordinate systems we must account for the fact that extra acceleration terms (for moving objects) may appear even in unaccelerated systems. Does this imply that authors who limit their discussions to Cartesian coordinates (or to “frames”, which implicitly entail a decision to "mod out" any difference in spatial coordinates while not modding out differences in time coordinates) are unaware of the existence of curvilinear coordinate systems, or that they would dispute the existence of such systems, or that they would dispute that extra acceleration terms appear in such systems even when not accelerated, or that they would dispute that those terms can be brought over to the “force” side of the equation of motion, just as can any other extra acceleration term? Of course not.Fugal (talk) 00:06, 29 August 2008 (UTC)

Does it imply that those authors believe that one extra acceleration term is somehow more physical or more “real” or more “mathematical” than any other acceleration term arising from the use of a coordinate system whose basis vectors diverge from inertial paths, whether it be in the spatial direction or the temporal direction or both? Of course not.Fugal (talk) 00:06, 29 August 2008 (UTC)

Does it imply that those authors fail to recognize that when an object moves relative to a given coordinate system, the extra terms that arise due to the variations in the basis vectors are literally the same terms, regardless of whether the basis vectors change in space at constant time or change in time at constant position (or both)? Of course not.Fugal (talk) 00:06, 29 August 2008 (UTC)

So, for this article to be written as if there are two inconsistent definitions is just a sophomoric misunderstanding, and just plain silly. The plain fact is that there is a fully general treatment of the subject, and then there are some fairly common simplified and restricted treatments of the subject, aimed at people who have no interest in the epistemological issues. This article goes out of its way to denigrate the more general and comprehensive treatment, and to dignify the simplified restricted treatment as the only “correct” one. That’s just a silly POV of one particular editor here, in support of which the article has become bloated with his own novel narrative and original research. I think (as others have suggested) that it would be helpful if that editor would take a break, and let people who have a mature understanding of the literature on this subject edit the article without being forced to engage in endless polemical discussions with someone who is has clearly lost perspective on this subject.Fugal (talk) 20:19, 28 August 2008 (UTC)

So you appear to be saying that Brews displays 'sophomoric misunderstanding' is 'just plain silly' and lacks a 'mature understanding' i.e. is immature. Please read and follow WP:CIVIL. Otherwise you may be taking a break soon yourself.- (User) WolfKeeper (Talk) 23:00, 28 August 2008 (UTC)

Brews has stated that my "ignorance of the subject is quite amazing". I don't recall you threatening him with blocking for such comments, nor would I wish you to do so. I do not take offence at these statements on this discussion page, because when someone believes that someone else is wrong, he has to say so. I ask no one to block him for saying what he thinks, even if he thinks I'm amazingly ignorant.Fugal (talk) 00:06, 29 August 2008 (UTC)

In comparison, I've stated here that it's "just plain silly" for the article to be written the way it is (for reasons which I explained at length), and I've stated that the current article represents a sophomoric misunderstanding of the subject, rather than a mature understanding of the subject. This is my essential critique of the article, and I explained in detail why I think this.Fugal (talk) 00:06, 29 August 2008 (UTC)

Now, it seems to me that your comment is intended to inhibit criticism of the way this article is written. If someone thinks an article is written based on misunderstanding, then they ought to be able to say so, and hopefully they will go on to explain what the misunderstanding is. And may I add that a majority of the editors have expressed views that are at least somewhat similar to mine, in terms of how the article seems to be slanted toward making some POV argument about the illegitimacy of the more general comprehensive view of the subject. There have also been multiple comments from multiple editors that two of the editors here have shown clear signs of thinking they have some ownership of this article, and ought to take a break, per the wiki guidance on "ownership".Fugal (talk) 00:06, 29 August 2008 (UTC)

I continue to think that some kind of mediation is needed here, i.e., some additional administrative oversight, before any real progress can be made. This latest attempt to intimidate editors and suppress comment on the quality of the article is a good case in point.Fugal (talk) 00:06, 29 August 2008 (UTC)

Your comments, Fugal, would be ever so much more interesting if they actually addressed the point. Of course, you can set up imaginary misinterpretations that are clearly so, and then claim that is what is happening here also. That approach of analogy to a "straw-man" is a rhetorical device used in debate, where the objective is to make one's point regardless of the strength of one's position. I'd suggest these gimmicks are out of place here. Address the actual situation; deal with the actual sources and citations.

It is impossible to dispute that there are two distinct usages for centrifugal. If dispute is attempted, it must show that in fact authors do not define fictitious forces that are non-zero in an inertial frame. Obviously, examples of this activity are already cited and cannot be made to go away.Brews ohare (talk) 14:10, 29 August 2008 (UTC)

Tags

{{Disputed|date=August 2008}} {{very long}} I think these tags should be removed. The first tag was placed by Fugal, and the issues he raised have been dealt with in the section of the article linked here. (He hasn't signed off on them, but also has not responded to suggestions for further discussion.) The second tag was placed by Timothy, who has not explained what exactly is too long about it, or what to do about it, and seems continually to insist upon exploration of advanced issues, with a tenuous (or, at least, vaguely identified) relation to the subject, requiring a still longer article to explain technical jargon (e.g. "tetrads", "congruence of timelike curves defined by constant spacelike coordinates", "continuous specification of the orientation of a spacelike triad to the timelike vectorfield"). Brews ohare (talk) 17:09, 28 August 2008 (UTC)

Strongly disagree with removing the tags with the article in its present condition. The majority of editors have expressed the view that the article is significantly too long, and that it contains misrepresentations and misunderstandings of the reputable literature. These have been fairly thoroughly explained on this discussion page.

One particular editor continues to misunderstand and misrepresent, and it seems clear to the majority of editors that this editor will never relinquish his position, no matter how clearly his misunderstandings are explained to him. This particular editor has adopted the tactic of filabustering, by reverting every edit that doesn't conform to his point of view, and justifying these reverts by posting endless repetitive objections to this discussion page based on his own misunderstandings, which he will never relinquish. Eventually every well-meaning editor simply gives up trying to reason with an obviously unreasonable person, at which point he declares victory and reverts their improvements back to his own misunderstandings.

Numerous editors have independently suggested that this particular editor appears to have strong feelings of "ownership" over this article, and they have suggested that it would be helpful for the article (not to mention for himself) if he would take a break. He shows no sign of taking this advice. As a result, the current tags on the article are necessary, and probably another should be added, about non-neutrality, since the article contains so much POV novel narrative and original research (all from this particular editor).Fugal (talk) 19:58, 28 August 2008 (UTC)

My own edits to this article are in direct response to this discussion page. They also have been supported in detail on this page, with repeated requests for commentary (as opposed to undocumented opinion). Brews ohare (talk) 05:39, 29 August 2008 (UTC)

Does the very long tag need explanation? The article is over 100k long! Note that the target is to try to keep article under 32k, for especially broad topics longer articles are exceptable. This article clearly does not fall in this last category. The fact that you couldn't figure that one out on your own says a lot about your loss of perspective with respect to this article. (TimothyRias (talk) 20:17, 28 August 2008 (UTC))

Not much help to say the article is long with no suggestions as to what should be changed to shorten it. Besides suggesting what might be cut, you might also suggest (i) why it should be cut and (ii) what might replace what is cut in the way of a more succinct explanation. Although you might debate the point, I'd say a good many of the additions to the article were provoked by the need for clarifications that you have occasioned yourself. Brews ohare (talk) 05:39, 29 August 2008 (UTC)

Wolfkeeper has adopted the policy of unilaterally deciding whether and when a dispute has been resolved, and/or whether it merits a dispute tag on the article. I believe this is contrary to Wikipedia policy. This behavior is especially egregious in the present case, because the majority of editors have expressed opposition to the POV that Wolfkeeper is promoting, and in fact at least FOUR editors have independently indicated that Wolfkeeper and/or Brews have lost their perspective and should take the advice given in the "ownership" article. In these circumtances, when a majority of editors have stated that an administrator has lost his or her perspective on a certain article, it seems to me that the administrator ought not to be exercising administrative functions related to that article (e.g., blockiing people who make unfavorable comments about the article). I wouldn't be surprised if there is already a Wikipedia policy stating as much, but even if there isn't, it sure seems like a reasonable idea. I'll try to contact some admin facilitators to see what they think, and report back.Fugal (talk) 04:57, 29 August 2008 (UTC)

A majority of editors??? Brews ohare (talk) 05:39, 29 August 2008 (UTC)

I forgot to mention that the inclusion of references in an article doesn't innoculate it against charges of being novel narrative. In fact, the description of novel narrative explicitly says that it consists of stringing together a bunch of references, but weaving them into a narrative whose meaning and intent differs from that of the sources. Hence it gets back to having a representative treatment, not simply citing references. The treatment must be accurate, and this is what is disputed in the present article.Fugal (talk) 05:01, 29 August 2008 (UTC)

Fugal: Your claim of narrative is totally unsupported by any documentation, and is simply invalid. The references are cited at enough length to show clearly that they are not misinterpreted in any way. Even longer excerpts can be read on line at the provided links.

In addition, your suggestions that a dispute exists on this talk page is not valid. A dispute implies dialog, and not just your own repeated statements. You have refused time and again to respond to all objections to your POV, and simply repeat yourself. And you have made no substantial, specific, documented objection to the article. Brews ohare (talk) 05:39, 29 August 2008 (UTC)

In my experience in 95+% of cases where an article is being tagged for POV, a general tag is completely inappropriate, and it's just a hissy fit of one editor to one or a few points being raised. This article is certainly no exception.- (User) WolfKeeper (Talk) 14:26, 29 August 2008 (UTC)

Concrete suggestions for reducing the length of the article.

OK, this article has grown way out of proportion. The current article size is over 100k. Not all of this is readable prose, but most of it is. (certainly at least 80k) We need to get this article back to readable proportions. Here are somethings that I think can be done to reduce the length:

1. The first 4 sections "Analysis using fictitious forces", "Choice of observational frame of reference", "Are centrifugal and Coriolis forces "real"?" and "Fictitious forces" contain a lot of overlap. Many of these sections repeat what has been said in the other section for a slightly different point of view. The sections can probably be rewritten to about 1 or 2 sections of about half the total length.
2. The discussion of artificial gravity from the "Are centrifugal and Coriolis forces "real"?" section can probably be removed. It doesn't really add anything to that section. It also opens up the more subtile subject of gravity itself being a fictitious force, which should probably be kept well beyond the scope of the article. It may be useful to re-add a small section on the subject of "artificial gravity" in the now very small "applications" section.
3. The "Moving objects and observational frames of reference" contains a long technical explanation of what local coordinates are, which is not within the scope of the article. The section would be better off referencing the appropiate article and skipping the long technical derivation.
4. On a similar note, a remark about the style of the article in general. Wikipedia as an encyclopedia not a textbook. The article has the strong tendency to try to explain and/or teach things. A more encyclopedic style of reporting facts about the subject would probably increase the readability of this article. This holds especially for long mathematical derivations to make a point. This will deter most potential readers. (mathematics may be a second (or first :)) language to (most) editors here, it certainly isn't for most readers) As a rule of thumb we should try to keep the use of formulas down to where the formulas themselves are the subject.
5. The "Uniformly rotating reference frames" is largly a paraphrase of the first section, but adds some actual formulas. (Which in this case are actually illustrative.) It should probably be taken along when rewriting/restructuring the first few sections.
6. The "Examples" section is probably a bit bloated. It should probably be condensed a little. It at least needs another look when the preceding sections have a more structured form.
7. The "Centrifugal force in polar coordinates" and the sections directly following it are a prime example of an editor falling in the pitfall of trying explain something. In this case it has lead to an essay several pages long trying make his point. The fact that a long the way the need arises to introduce new nomenclature should be seen as writing on the wall. Nowhere in the cited literature is connection/difference between the two "types" of centrifugal discussed, hence the wikipedia article should not either. Any attempt to discuss either - without any direct reference to a reputable source discussing this precise topic - will result in some form of original research.

(I'm out of time for the moment, I'll be back to elaborate on this last point some more.) (TimothyRias (talk) 10:31, 29 August 2008 (UTC))

I agree. Timothy has presented a good plan for trimming the article down to a more manageable size without losing any crucial content. In particular, I agree that the entire "centrifugal force in polar coordinates" major section can be removed entirely, for the reasons he states above: I have therefore WP:BOLDly done so. -- The Anome (talk) 11:57, 29 August 2008 (UTC)

Anome: Well, advancing matters to an edit war with absolutely no discussion is a very forward step. Your failure to remove the curvilinear section which logically also should go for the same reasons (although improper reasons) shows your lack of care in looking at this matter before so BOLDLY stepping into this matter. I fixed that for you. I congratulate Fugal and Timothy for having achieved their goal of censoring a very clearly argued case, never responded to in any way by these two editors, who have merely ranted on and on. Great editing Anome. Great. Real leadership. Glad you are so BOLD as to simply cut the knot, grasp the nettle etc. etc.. Brews ohare (talk) 14:43, 29 August 2008 (UTC)

Thanks for that: the curvilinear section was the next to go, and I'm glad you've preempted me by removing it as well. My intention was just as you said: to grasp the nettle and cut the knot. I'd be glad to help work on the rewrite of the rest of the article, as per Timothy's plan. -- The Anome (talk) 01:12, 30 August 2008 (UTC)

Many of Timothy's suggestions bear examination. I hope his later contributions undertake to explain just what he suggests in more detail. A massive rewrite like this is an undertaking, and as what is being replaced has been through numerous revisions, I suspect any replacement will as well. Brews ohare (talk) 13:57, 29 August 2008 (UTC)