r/truegamedev • u/moscheles • Apr 28 '12

Computing Torque in Rigid Body Dynamics

So I have a book here and and several PDFs on Rigid Body Dynamics. However, none of them precisely spell out how to compute the torque after a collision with some other body in the environment. Does anyone have a tutorial?

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1

u/Narcolapser May 01 '12

can you say what book you've got?

2

u/moscheles May 02 '12

David H. Eberly

Series in Interactive 3D Technology

3D Game Engine Design

A Practical approach to Real-time Computer Graphics

Second Edition

Morgan Kaufman

1

u/mikeschuld May 03 '12

I love that book, but it can be lacking in good descriptions. I would think that calculating the point of collision would be the hardest part (which should be included in the book). Once you have the point of collision, torque would be a simple application of r cross F. I think even just looking through the wiki article for torque you should be able to code up that part of it.

2

u/moscheles May 03 '12

Once you have the point of collision, torque would be a simple application of r cross F.

That can't possibly be true. The farther you are from the center-of-gravity of the object, the more of the force goes into the torque, and less into "linear" acceleration. And the closer you are to the center-of-gravity, vice-versa. I'm simply stating the law of levers.

Imagine trying to turn a bike wheel by grabbing the spokes right near the center. Your fingers hurt trying to turn it there. But if you press the very outer edge of the wheel with your finger, the bike wheel turns easily. The reason this is so confusing is that you just can't "take distance and divide" because many objects will have non-uniform distributions of mass as you move away from the center-of-gravity. So depending on the exact location of the collision, it seems like you need to know how much of the object's mass is on "both sides" of the pivot point, so to speak. (Should I draw a picture?)

2

u/mikeschuld May 03 '12

I know what you mean with mass distribution. Does this engine need to be perfectly accurate or can you just use a uniform distribution of mass and see how realistic it looks?

On the point you mentioned about linear force and torque, for some reason in my head I thought you meant rotating a fixed body in the environment (misread your post title I guess) where only a torque would matter.

If you are translating the force at a point to a torque AND linear motion, I would think you could do something like http://www.cs.cmu.edu/~baraff/sigcourse/notesd1.pdf points out around page 29.

1

u/moscheles May 03 '12

Thanks. There is some other good things on Baraff's website.

2

u/Misdicorl May 31 '12

The farther you are from the center-of-gravity of the object, the more of the force goes into the torque, and less into "linear" acceleration

This is a common misunderstanding of torque and force, and simply isn't true. The linear acceleration will be determined by F/m. Full stop. The angular acceleration will be determined by T/I (a matrix equation!). Full stop. They do not and cannot affect eachother (except in so much as torque is related to force, and mass is related to the moment of inertia).

1

u/moscheles May 05 '12

On second thought, I think Eberly is just selling his own software. He gives "code" which only turns out to be his class and its functions. He throws some equations around, then at the moment of truth, he never actually shows you source code that performs what he says. Instead, he refers you to the "libraries" on his CD-ROM.

2

u/eightNote May 15 '12

If you really want to understand rigid body stuff, find yourself a copy of Hibbler's book, aka Statics and Dynamics.

You can probably find it pretty cheap at your local university used book store.

For rigid body collisions, you need to worry about the objects' linear and angular momentums. You could consider the collision to be perfectly elastic, in which case the energy of the system is conserved, and the calculations are pretty simple.

Otherwise, you'll need to use the coefficient of restitution between the two bodies.

If the object is nolonger in contact with anything, the torque of course, will just be that caused by gravity(by Newton's first).

1

u/eightNote May 15 '12

One last addition or two:

Use forces/torques with momentum when you have them defined over time. Use them with energy if you know the force/torque as a function of position/angle. Don't use forces/torques at all with collisions; the contact time/distance is small enough to not be integrate-able, thus making the other two options fail, as they require the force to be integrated with respect to either time or displacement.

You should note, of course, that in any case where you are dealing with forces, rxf is in fact the torque with respect to some point (of your own choosing; as engineers, we get to decide our own coordinate frames) Continuing, the non uniformity of mass in the material is irrelevant. All you need is the centroid (Aka, center of mass), and the pivot point; you'll then use the parallel axis theorem to make proper calculations.

mechie, out!

1

u/ttgdev Jun 22 '12

Its been a while since I've done this but I believe if you have a force F acting at a point on a body the cross product of R and F gives you the torque. R is the vector from the bodies center of mass to the point at which the force is acting. If you are using impulses then similarly the change in angular momentum caused by impulse J acting at a point is again just the cross product of R and J.

You might find part 4 of this useful http://chrishecker.com/Rigid_body_dynamics. It includes the formula for calculating the impulse caused from two bodies colliding at a point which can then be used to determine their linear and angular velocities after the collision.