Talk:Displacement (geometry)

Position and Displacement

I have tried to introduce some consistency with the use of the word "displacement". The big issue is that velocity should be the rate of change of position and not the rate of change of displacement. Also it is better to use x for position in one dimension, r for position in three dimensions and then Δx or Δr for displacement in one or three dimesions respectively. I try and avoid the previously common practice of using "s" for displacement as this tends to hide the fact that displacement is indeed a change in position. However I have had some difficulty in inserting the Δ in some of the formulae and so I have not be able to complete the change from "s" to "Δx" in all the formulae.Phillip (talk) 12:04, 23 December 2008 (UTC)

This is something that also needs to be corrected in the infobox at the bottom of the page. —Anonymous Dissident^Talk 11:21, 5 March 2009 (UTC)

I disagree. I think we should start with (linear) displacements (as actions) and then velocities are rates of displacement and position vectors are displacements of/from a defined origin. Note especially that we can define velocities without defining either a coordinate system or an origin point.

Note then that one needn't define displacements in terms of a coordinate system but purely as actions on a space of points. Then position vectors are defined in terms of an origin point and displacements and ultimately (rectilinear) coordinates are defined by the origin and by the basis on the space of displacements.

Regards, James Baugh (talk) 21:36, 9 January 2010 (UTC)

I have edited the introductory definitions to reflect displacements as independent of origin and thus of position vectors. In geometry we do not need a coordinate system or origin to define a displacement. I think there may be too much tangential material on velocities etc but didn't cut, only rephrased. I also dropped the comment on the link to affine space since the point space in which we define displacements essentially is an affine space. We are not distinguishing displacements from positions there but rather here... they are already distinct. The space of displacements is the translational component of affine transformations on a geometric space.

This article still needs some work. I'll look back later and see if I can tweak further and add references. Regards, James Baugh (talk) 22:36, 9 January 2010 (UTC)

Clarifications

Is it safe to say that if I am 1.5 meters tall, that quantity(1.5) is NOT a vector? Also, is it safe to say that if, since I was a zygote, that my height increased by 1.5 meters, that quantity(1.5) IS a vector? —Preceding unsigned comment added by 75.23.226.176 (talk) 00:32, 18 June 2008 (UTC)

No - that would not be an example of a vector. A vector is a quantity that has both a magnitude and a direction. It does not depend on a quantity changing. Suppose there is a town exactly 100 miles north of where you are now. The statement that the town is 100 miles away from where you are is not a vector. The statement that the town is 100 miles north of you is a vector quantity. Hope this helps. PhySusie (talk) 12:28, 22 June 2008 (UTC)

Magnitude + direction is actually the naive definition of a vector. To truly be a vector it must transform in the right way, Position "vectors" do not transform in the right way, displacements do.-DB

Old

Is there any useful application of the integral of displacement with respect to time? 82.15.224.87 20:26, 21 November 2006 (UTC)

Not particularly. There are useful applications of the integral with respect to arc length, as in finding the distance traveled, or in integrating functions over the path. But simply with respect to time, I cannot think of any.Corkgkagj (talk) 15:41, 3 January 2008 (UTC)

Hmm, if peeople can come up with jounce, crackle and pop they should go the other way too. For completeness sake any references for a term that could go to the left of displacement in the kinematics template?83.146.15.7 (talk) 20:28, 11 April 2009 (UTC)

Calculating Displacement

These can be used to calculate displacement where u=initial velocity, t=time, a=acceleration, v=final velocity $r={ut+{1 \over 2}at^{2}}$ $r={1 \over 2}(u+v)t$ hylian_loach 12:11, 20 April 2007 (UTC)

I wasn't sure whether to add it into the article not knowing if it was listed in another, or unsuitable.hylian_loach 12:13, 20 April 2007 (UTC)

Why don't you add it? It's what I was looking for, it's vital for physics. LOTRrules (talk) 19:12, 10 February 2008 (UTC)

I've added the additional sections as I thought the previous sections are a little confusing. I've added something about height and the relation to the equations of motion. LOTRrules (talk) 19:54, 10 February 2008 (UTC)

First sentences

The first sentence in the intro is: "A displacement is a relative motion between two points independent of the path taken."

It is true that a displacement of a point P is a "relative position" of P, i.e. the final position of P relative to its initial position. The expression "relative motion between two points" is not the best way to express this concept.

The second sentence is: "The displacement is thus distinct from the distance traveled by the object along given path."

Here, the use of italics typeface is misleading. The reader might think that a displacement is not a distance. On the contrary, it is a distance imaginarily traveled along a straight line, distinct from the distance (actually) traveled by the point.

The third sentence is: "The displacement vector then defines the motion in terms of translation along a straight line."

Here, the word "translation" is misused. This word refers to the motion of a rigid body, which does not rotate (i.e. does not change its orientation in space). Here, we refer to the motion of a point, and a point does not have an orientation in space.

I rewrote these sentences. Paolo.dL (talk) 21:57, 8 February 2010 (UTC)

`distance vs displacement` diagram

The diagram shows the difference between the taken route (the path) and the shortest route (as the crow flies), but doesn't show the difference between the scalar (distance) and the vector (displacement) very well. The diagram implies that distance is only used for paths; which is false as it can be used on straight lines. --86.165.94.3 (talk) 15:58, 29 September 2010 (UTC)

The "snap/crackle/pop" survives

The crackle page has been successfully deleted, but the snap/crackle/pop survives on Wikipedia here and else where. I have never heard of the 4th, 5th and 6th derivatives of position referred to in this way until I came across the page on Wikipedia. Has anyone else ever heard these terms used in any class, book or talk?

It is definitely not Wikipedia's place to introduce new terminology. If a suitable source for these terms can not be found I would like to systematically remove them from Wikipedia.

Phancy Physicist (talk) 07:44, 30 May 2011 (UTC)

There were references to the term in published books in the deleted article. The term has certainly been used in academia. I don't see any advantage in deleting it altogether. Szzuk (talk) 22:28, 2 June 2011 (UTC)

The reason I want to remove it so badly is that if it is not the accepted terminology but it is on Wikipedia anyways, people might start using it as if it was. All references I have found supporting "snap/crackle/pop" all come back to this [[1]]. And in the text of this page I see:

"Another less serious suggestion is snap (symbol s), crackle (symbol c) and pop (symbol p) for the 4th, 5th and 6th derivatives respectively." and "Needless to say, none of these are in any kind of standards, yet. We just made them up on usenet."

I am really am a physicist by trade and have been to many talks, and in many mathematics and physicist classes, even taught a few. I have never heard or seen these terms used by anybody but people who reference Wikipedia or the above page. If I am wrong so be it but I want proof.

I am not attacking Szzuk by any means. I thank them for responding. But what I am looking for is a book or something very reliable to support the use of these terms.

Phancy Physicist (talk) 03:22, 3 June 2011 (UTC)

Comment. Ask the deleting sysop to send you a copy of the deleted article and you can add the refs yourself. Szzuk (talk) 13:03, 3 June 2011 (UTC)

In January 2012, this issue was mentioned on the Science Reference Desk (here). As I stated verbatim on the desk:

Wikipedia is not an indiscriminate list of any term anybody ever used to describe anything. Those names are uncommon. I have removed them from the article, and replaced the section with a discussion, including cited sources.

I have rewritten the section and cited a reliable textbook. The burden of evidence is on anyone who wishes to re-add these uncommon names for higher-order terms. Nimur (talk) 21:53, 2 January 2012 (UTC)

Seems to be used repeatedly in research literature. E.g.

• Sprott, J. C. "Some simple chaotic jerk functions." American Journal of Physics 65, no. 6 (1997): 537-543. Cites usenet: "These terms were suggested by J. Codner, E. Francis, T. Bartels, J. Glass, and W. Jefferys, respectively, in response to a question posed on the USENET sci.physics newsgroup."
• Visser, Matt. "Jerk, snap and the cosmological equation of state." Classical and Quantum Gravity 21, no. 11 (2004): 2603.
• Eager, David, Ann-Marie Pendrill, and Nina Reistad. "Beyond velocity and acceleration: jerk, snap and higher derivatives." European Journal of Physics 37, no. 6 (2016): 065008.
• Hayati, Hasti, David Eager, Ann-Marie Pendrill, and Hans Alberg. "Jerk within the context of science and engineering—A systematic review." Vibration 3, no. 4 (2020): 371-409.

–jacobolus (t) 22:45, 10 February 2023 (UTC)

shot and put (9th and 10th derivatives)

I read about "shot" and "put" at the jounce page, and I wanted to add them here, but they start with letters some previous derivatives start too, so I don't know what symbol to put! any suggestions? — Preceding unsigned comment added by 78.0.232.28 (talk) 09:25, 2 September 2011 (UTC)

perhaps 'motion' should be dropped from the definition

While the concept of displacement is used in physics to describe motions of objects, it seems to me that the basic definition should be more general; in practice the term refers to any vector difference between two points in an affine space (not necessarily metrical). That is, if we have two affine points $P$ and $Q,$ we can call the quantity $v=Q-P$ the displacement or displacement vector from $P$ to $Q$ without necessarily needing any specific path between them. The same displacement can then serve as a translation of the affine space when added to arbitrary other points, e.g. $P'+v=Q'.$ (While it is not a priori meaningful to add affine points, except as sums like $(1-t)P+tQ,$ subtracting them to obtain a displacement is unambiguous and relatively common notation.) –jacobolus (t) 21:30, 10 February 2023 (UTC)

@D.Lazard pointed out elsewhere that the term displacement often (originally?) more generally refers to any rigid transformation, not just translations but also rotations and screw displacements, and according to some authors also improper rigid transformations. But I have also seen displacement vector used to mean the vector difference between points, a synonym for translation vector, as described in this current article. I wonder if this should be moved to displacement vector or possibly translation vector, and more general concepts of "displacement" directed to rigid transformation. –jacobolus (t) 23:04, 17 January 2024 (UTC)

IMO, this article must be moved to Displacement vector, and the article must say that in some contexts, this is abbreviated to "displacement"; Displacement (geometry) must be a redirect to Rigid motion. In fact, a displacement vector characterizes the action of a motion on a single point, and it equals the translation vector when the motion is a translation. In French, a déplacement (displacement) is the standard name for a rigid motion (the literal translation in French of "rigid motion" sounds very odd). However, I do not know whether "displacement" is used in this sense in reliable English sources. I do not believe that "displacement" has ever been used for improper rigid transformations. It must be emphasized that the concept of a "displacement vector" is useful in the context of motions that are not rigid transformations, such as in fluid mechanics.

If I was not bold, and did not make these changes myself, it is because I am not sure that French and English terminologies are similar in this case. D.Lazard (talk) 11:20, 18 January 2024 (UTC)

Looking at literature about kinematics in English (not sure about other fields), the word displacement is definitely used to mean the same as motion or rigid transformation (we may want to also merge those pages, or figure out more carefully what the scope for each should be). While we're at it screw axis should be moved to screw motion (with screw displacement, screw transformation, helical motion, etc. redirecting there), and should be rewritten to focus on the transformation rather than the axis specifically (though the axis should be mentioned), with a section about screw symmetry (a.k.a. helical symmetry) which could plausibly be expanded into its own article if anyone wants to write one someday.

In skimming quickly around, a while ago, I wasn't super careful about tracking individual sources, but I think some of the time the definition for either "motion" or "displacement" was to mean only proper (orientation-preserving) isometric transformations, and other times the definitions also included improper (orientation-reversing) isometric transformations. Proper transformations are noteworthy because they can be smoothly arrived at from the identity transformation, whereas improper transformations involve both some smooth transformation and also an extra reflection somewhere along the way. –jacobolus (t) 16:00, 18 January 2024 (UTC)

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