# coefficient of restitution question

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Is it possible to express the coefficient of restitution as forces applied to the colliding particles, instead of new velocities? I'm using the formulas here (under the "use" section) http://en.wikipedia.org/wiki/Coefficient_of_restitution

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A force has to act for some amount of time in order to change a particle's velocity. If the results of the collision are to be instantaneous, then applying a force won't do. There is a notion of "impulse" that might be what you are looking for.

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The coefficient of Restitution is a kinematic law, that is, it doesn't use forces. To find the forces (you probably mean impulse, since you're probably using a "force" based physics engine with time steps, right?) involved, you need to work backword.

To find the impulse on the particle, find it's change in velocity and multiply that by it's mass. Ie:

I (Impulse) = (final velocity - initial velocity) * particle's mass

Do that for both particles and you have your "forces".

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Something similar to a coefficient of restitution on the force level is for instance when simulating particles with a spring force to introduce a damping term, something like force = springconstant*overlap - viscosity*velocity when the particles are overlapping.

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Numsgil, Thanks for your reply. I believe you wrote that wiki article right? It's excellent.

So I would still need to find the new velocity but I could apply it as an impulse to the particle using:

((velocity after collision) - (velocity before collision)) * mass

In my verlet sim I apply forces in the integration loop simply by adding the (accumulated forces * deltaTime2) to the current velocity of each particle. This appears physically accurate, but I'm not sure if they have a basis in correct physics along the lines of the COR (which I'm using as well for collision response)

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