Regular and chaotic dynamics in bouncing ball models

Vogel S., Linz S. J.

Abstract

One of the prime paradigms for complex temporal dynamics, the motion of an inelastic ball bouncing on a sinusoidally oscillating table, is revisited. Using extensive numerical simulations, we address the not yet conclusively settled problem of the occurrence of chaos in the partially elastic case. We systematically investigate the spectrum of long-time solutions as function of the initial conditions and system parameters. Subsequently, we generalize the bouncing ball system by taking the velocity dependence of the coefficient of restitution into account and exemplarily demonstrate the drastic impact of such a generalization on the overall dynamics