Talk:Trochoid

Confusion in the definition

The article states that "A trochoid is the curve described by a fixed point on a circle as it rolls along a straight line", but then goes on to talk about cases where the point is *inside* the circle or *outside* the circle. So there is something inconsistent or at least ambiguous about the definition. It is not at all clear what the difference between a trochoid and a cycloid is. Perhaps the idea that for a trochoid, the fixed point is on one circle but a different concentric circle is the one rolling along the line? ie. the circle with the point we're tracing out is not necessarily the same radius as the circle that is rolling on the line - but it moves and turns at the same rate? 203.188.220.250 (talk) 01:28, 6 October 2016 (UTC)[reply]

Epitrochoids & Hypotrochoids

According to the OED, "trochoids" include epitrochoids and hypotrochoids, at least by extension. This general class could be expressed in parametric form (parameter t) as:

{\begin{array}{lcl}x&=&x_{0}+r_{1}\cos(\omega _{1}t+\phi _{1})+r_{2}\cos(\omega _{2}t+\phi _{2}),\\y&=&y_{0}+r_{1}\sin(\omega _{1}t+\phi _{1})+r_{2}\sin(\omega _{2}t+\phi _{2}),\\&&r_{1}>0,r_{2}\geq 0,\omega _{1}\neq 0.\end{array}}

With $\,\phi _{2}=0,r_{2}\gg r_{1},\omega _{2}t\ll 1,$ and $\,r_{2}\omega _{2}t$ moderate, this reduces to a "straigt-line" trochoid:

{\begin{array}{lcl}x&\rightarrow &x_{0}+r_{1}\cos(\omega _{1}t+\phi _{1})+r_{2},\\y&\rightarrow &y_{0}+r_{1}\sin(\omega _{1}t+\phi _{1})+r_{2}\omega _{2}t.\end{array}}

The signs of the variable terms in the above equations can be changed two ways: by changing either angular phase term (φ) by 180° or by changing the sign of either angular velocity (ω), such that these expressions are inclusive of all combinations of signs in their summation terms. Toolnut (talk) 15:30, 14 July 2011 (UTC)[reply]

Trochoidal wave

In 'Seaworthiness' (about dynamic stability of ships) Marchaj writes about trochoidal waves, a description of the movement of water when a wave passes by. As I understand it, the water follows a circular motion, in the direction of the wave at the crest and in the opposite direction in the trough. This might be a nice addition to the article, as a real life example.
However, this circle becomes smaller with depth, and that I don't understand. Do the circles overlap? Then how does the water move?
I wanted to upload his illustrations, but I've been criticised before for uploading non-free photos (even from the family album), so I decided not to take the risk. DirkvdM (talk) 13:58, 11 October 2011 (UTC)[reply]

[1] has a nice summary of what you're talking about. I think the idea is that the 'wave curve' is approximated better by a scaled trochoid than a sine wave. It appears these approximations are not true trochoids but are stretched horizontally. Also, the limiting case for the trochoid would be the cycloid, but according to the web page actual waves become unstable well before reaching that limit.

To answer your question, the circles overlap in space but not in time. So the paths of two molecules of water may intersect, but they occupy the point of intersection at different times so this is still physically possible.--RDBury (talk) 15:55, 11 October 2011 (UTC)[reply]

Thanks. Yes, of course, if, say, the waves move to the right, at the crest the water molecules move to the right, then as the wave passes they move down until their 'location' (the circle they move in) becomes a through, where they move to the left and then they go up again. The different directions of movement in the circle take place in different locations along the length of the wave.

Your link possibly resolves another problem I thought of yesterday. Take two molecules, one below the other. Assuming the angular velocities (the rotation frequencies) of their circles are the same, they wil stay in the same relative position and move around together. But since the lower circle is smaller, in a trough they will be closer together than at a crest. But that can't be because water is not compressible. But this can be resoved if the molecules move horizontally, relative to each other, in the direction of wave movement. The linked article says that as a wave has passed, the water has moved slightly in its direction. If this movement differs for the two molecules, that could resolve the issue. I assume the upper molecule will move faster.

By the way, if lower circles are flatter, as the article says, this effect increases (they will be closer together at the bottom). Now in so far as it is the presence of a seabed that causes the lower circles to flatten (and the oddly named wind wave article supports that), the closer inshore there will be more flattening and a greater difference in 'real' forward motion between lower and higher circles, which is in tune with what the article gives as a reason for the breaking of waves. Which is not to say that's the (only) cause, but it fits.

Since the wind wave article doesn't mention trochoidal waves I'll bring it up at that talk page, also referring to this thread. DirkvdM (talk) 08:42, 13 October 2011 (UTC)[reply]

some help here

I am making a computer program, and it involves trochoids. Could someone explain what all the variables in the formulas mean, and maybe do an example out? That would be amazing.

thanx in advance 71.195.89.255 (talk) 00:59, 27 January 2013 (UTC)[reply]

Are you sure about the "more general" approach?

The article says:

--- A more general approach would define a trochoid as the locus of a point ... orbiting at a constant rate around an axis located at ... ... which axis is being translated in the x-y-plane at a constant rate in either a straight line ... ---

Where did you get this? I never saw such a generalized definition of a trochoid. I have always seen trochoids defined as curves traced by a *fixed* point on the rotating plane etc etc. I would be very interested in seeing a reference for the above "more general approach". — Preceding unsigned comment added by Go 62 (talk • contribs) 10:26, 24 July 2013 (UTC)[reply]

Inquiring

isn't that the function y=abs(sin(x))? Cause it sure looks like it. I do not know; I am asking. — Preceding unsigned comment added by 68.150.250.66 (talk) 06:39, 23 January 2014 (UTC)[reply]