Patrick Elliott wrote:
> I am looking at a situation in the future where I plan to simulate an
> entire area that is rotating, like a big drum. This will be done by
> simply having the wall texture on the entire outer surface drift, as
> though its spinning. But, I also want to place a suspended rail tram in
> there, and have it react (sadly, due to the limits of the system, only
> with one angle, since I can't have more than one pivot point), as though
> its being effected by the rotation, as well as its changes in momentum.
> I am presuming that the math for this has to be:
>
> http://www.myphysicslab.com/pendulum_cart.html#navsite
>
> But.. then I run into a problem... Basically, I am not sure what the
> frak is going on there...
>
It looks to me like you might have a modelling problem to figure out first. Are
you talking about something like the following, with the track attached to the
inside of a rotating drum instead of the surface of the earth? Is there any
actual gravity?

http://www.nycsubway.org/wiki/Wuppertal,_Germany

The important thing here is whether the tram swings in the direction of its
motion (as in your link), or whether it only swings significantly from
side-to-side (as in the link I posted).

> Biggest issue is, there is a lot of stuff in it that won't help me.
> Friction.. Well, no, the cart isn't going to be controlled via "forces",
> its running a plotted course, so half the stuff in the "force of the
> cart" part is just flat out meaningless. Then there is the fact that my
> force calculations need to be only the force that its being applied "at
> that moment" in one direction, two 3D vectors. That one is going to give
> me issues, as it is. But, maybe I can direct substitute it in as F, or
> something. Do I assume the cart mass itself is 0?

If I have managed to get the gist of what what you're modelling, you might be
able to reduce your system to a single degree of freedom, vastly simplifying the
math. (Sort of, you would only need to solve for one unknown.)

> Why can't there ever
> be a simple, "Someone did this once, for a very similar situation, so
> here is the math, and all you need to do in integrate the other rotation
> thing you are doing." You know, instead of googling, and getting page
> after page of descriptions, without math, of the things, or articles on
> control systems, without math, for them, or just about anything other
> than an explanation of how the frak it works in a real world, 3D
> situation. lol
>
I'm completely with you here. I do whacky math for a living, and it is
tremendously difficult to find out if someone else has solved a problem I'm
doing. Not only would I like to check my work, I also need to properly cite the
original author if I end up publishing something about it.

> At the very least, some idea what I can/should do to cut extraneous data
> out of the equations I do have, would be helpful. I am just real glad
> the "pendulum" is going to be "one directional" just like the example,
> and not with two axis of rotation, like.. a lot of them have.

If I'm on the right track here, I personally wouldn't use either of the
approaches in the link you posted. What makes your problem quite different from
what thousands of mathmaticians, physicists, and engineers have solved countless
times over the years is the rotating coordinate system inside the drum. Plus,
the local coordinate system of the tram is varying along its (rotating) path.

However, I'm still not certain if I'm thinking about the same problem you are.
Are you trying to come up with an exact symbolic solution, perhaps so you can
design a control system? Or, do you just need a reasonable numerical
approximation, perhaps just for animation?

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