## Quick Reference

A parameter associated with the behaviour of two bodies during a collision. Suppose that two billiard balls are travelling in the same straight line and have velocities *u*_{1} and *u*_{2} before the collision, and velocities *v*_{1} and *v*_{2} after the collision. If the coefficient of restitution is *e*, then

*v*_{2}−*v*_{1}=−*e*(*u*_{2}−*u*_{1}).

This formula is Newton's law of restitution. The coefficient of restitution always satisfies 0≤*e*≤1. When *e*=0, the balls remain in contact after the collision. When *e*=1, the collision is elastic: there is no loss of kinetic energy.

It may be convenient to consider a collision as consisting of a deformation phase, during which the shape of each body is deformed, and a restitution phase, during which the shape of each body is completely or partially restored. Newton's law follows from the supposition that, for each body, the impulse during restitution is *e* times the impulse during deformation.

*Subjects:*
Sports and Exercise Medicine — Mathematics.