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# coefficient of restitution

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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 u1 and u2 before the collision, and velocities v1 and v2 after the collision. If the coefficient of restitution is e, then

v2v1=−e(u2u1).

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.

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