Coefficient of restitution of a linear dashpot on a rigid surface

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.

Numerical simulation of non-central collisions of spherical magnets

“…Using this damped spring approximation allows the contact force to become attractive, which is unphysical [10]. However, in driven collisions with low damping, this issue can be compensated by the choice of the damping parameter [12]. Further, we are more concerned with the final state when the collisions have ended, which is unaffected by the details of the contact force.…”

“…The translational (18) and rotational (19) equations of motion are solved in parallel. The torque (12) is already accounted for by the force equation, and does not need to be solved separately.…”