Coefficient of restitution ($e=\frac{\text{normal separation speed}}{\text{normal approach speed}}$)

The restitution law applies to velocities of the actual contact points, including any rotational velocities of rigid bodies. A perfectly elastic collision has $e=1$; $e=0$ gives zero immediate normal separation speed, but does not by itself require all parts of colliding bodies to share the same velocity.

// Target: classical-mechanics.bigb

For repeated vertical collisions with a fixed plate and constant coefficient of restitution $0\le \gamma <1$, each collision multiplies the upward speed by $\gamma$, so successive peak heights form the displayed geometric sequence. The initial fall plus both legs of every rebound have total distance $h_0(1+{\gamma }^2)/(1-{\gamma }^2)$. The idealized impact times accumulate in finite time when $\gamma <1$; real contact mechanics replaces the limiting sequence by rest.