# [Physics] Forces and rotation

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Hey all, this is my first post. I've been experimenting a bit with physics simulation, i'm currently using euler and it's all going well untill now. I'm thinking about how to implement angulair velocity in my game but im not sure about the method. I had the following idea: Above is the 2D representation of the problem, a point (p) is attached to another fixed point (Center of mass for example, point m) it's sort of a pendulum you could say. The general problem: A force is aplied to the point, what will be the rotation velocity and rotation matrix/quaternion (not sure what to use yet, ill get back to that later). My solution: The arbitrary axis around which the point will be rotated will the CrossProduct of vector v (from COM to point) and F (force). the effective force f, will be the cosine(anglebetween((v and F) - 90 degrees)) where anglebetween(v and F) will be the DotProduct of these two vectors. After this i divide the force f by the mass of the point to get the acceleration. The angulair velocity will be (circumference O / force f.length) * 360 degrees. My problem: Are these calculations correct and most important, is there an more efficient way? (they seem to be correct since i tested them sort of, with quaternions, and it acts like a pendulum). Since i have the angle and arbitrary axis using a quaternion for my rotation seemed most logical but i'm not sure this is the best way to solve this problem and how to use a unit quaternion in combination with 'realtime' (time elapsed between this and last frame). I hope my explanation and questioning makes sense, Sincerly, Scorpie [Edited by - Scorpie on April 5, 2006 1:16:49 PM]

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Whether or not your current equations are correct (some of it looks right, but I didn't look carefully), this is a wheel that you probably don't need to re-invent; the equations of motion are already well established and documented. Too lazy to dig up links at the moment, but you can find papers online by David Baraff and Chris Hecker, respectively, that go over all this in great detail.

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