Coefficient of restitution

The coefficient of restitution measures the ratio of relative speed after a collision to relative speed before it, along the line of impact. It describes how much kinetic energy is dissipated in that direction.

Newton's law of restitution: A collision relation stating that separation speed along the impact line equals the coefficient of restitution times approach speed. This equation defines how the coefficient links pre-impact and post-impact velocities.
Relative velocity: The velocity of one body measured relative to another body. Restitution compares the colliding bodies' relative velocities before and after impact.
Bouncing ball: A ball that repeatedly strikes a surface and rebounds under gravity. Successive rebound heights can estimate its coefficient of restitution.
Superelastic collision: A collision in which relative kinetic energy increases because stored internal energy is released. Its effective restitution exceeds one, unlike ordinary dissipative impacts.
Impulse: The change in momentum produced by a force acting over a time interval. Contact impulse changes each body's velocity during the collision.
Elastic collision: A collision in which total kinetic energy is conserved. An ideal one-dimensional elastic collision has a coefficient of one.
Drop test: An impact test that drops an object onto a surface to measure its rebound or damage. A controlled drop provides an experimental estimate of restitution.
Viscoelasticity: Mechanical behavior combining elastic response with time-dependent energy dissipation. Viscoelastic contacts can make restitution depend on impact speed and material properties.
Line of impact: The direction along which colliding bodies exert their principal contact impulse. Restitution compares relative velocities only along this direction.
Inelastic collision: A collision in which total kinetic energy decreases during impact. Most real impacts have restitution below one because some kinetic energy is dissipated.

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