Coefficient of restitution of a linear dashpot on a rigid surface

TL;DR

This paper investigates how gravity affects the coefficient of restitution for a bouncing ball modeled with a linear dashpot, revealing velocity dependence especially at low impact speeds, and proposes a hybrid collision model that aligns with experimental data.

Contribution

It introduces a hybrid collision model combining previous approaches, accurately capturing velocity-dependent restitution influenced by gravity.

Findings

Coefficient of restitution depends on impact velocity when gravity is included.

The hybrid model reproduces experimental bouncing behavior.

Velocity dependence is most significant at low impact velocities.

Abstract

The linear dashpot model is applied to a single ball bouncing on a rigid surface. It is shown that when gravity is included the coefficient of restitution depends on impact velocity, in contrast to previous work that ignored the effects of gravity. This velocity dependence is most pronounced at low impact velocities and high damping. Previous work has considered the ball to be in contact with the floor when the compression is nonzero, while other analysis terminates the collision earlier, to prevent an attractive force. We compare these models and propose a hybrid between the two. The hybrid model is successful in reproducing experimental results for a cart bouncing repeatedly on a spring.