# How to calculate the coefficient of restitution for 2 bodies?

I have 2 rigid bodies (from different materials) in a collision.

As you know I should have the coefficient of restitution value to get the velocities after collision.

What is the information/values should I know about each body to calculate the restitution? And how to calculate it?

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Except in special cases it would be very hard to calculate the Coefficient of Restitution from first principles. The Coefficient of Restitution is not a fundamental property like mass or internal energy. It's a way of describing energy losses in the colliding bodies, but the energy losses can arise from all sorts of causes. It's probably not even constant and will depend on the energy of the collision.

Did you have a specific system that you want to calculate the Coefficient of Restitution for?

JR

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i am making a physics Engine , i thought that there is 2 constants (one for each material) can be used in a LAW to calculate restitution of the 2 bodies/materials – MhdSyrwan Jan 30 '12 at 23:19

Game engines typically do approximations that may or may not relate in anyway to reality. For example CORs typically reduce with increasing velocity, but that's typically left out of games. I've seen game engines just take an unweighted average CORs of two impacting objects. A physically more realistic approach would be to do a weight the average of the CORs by the inverse of the stiffness of the objects.

Of course the COR and stiffness of each object depend not just on the material but the geometry. Even within a single object the location of the impact will change the COR and stiffness. A tuning fork, for example, has a very low stiffness on the outer tip of the fork, but a high stiffness on the joined end. To properly account for these variances one could do an FEA analysis on each object to create a COR and stiffness map that could be used by the physics engine.

However, unless realistic physics is important to the workings of the game, a single COR for each material type, and a weighted or unweighted average will probably be fun and look mostly realistic.

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