Paradoxical simulation results of chaos-like chattering in the bouncing ball system

Memorial

This paper was finalized just before the death of Kilian Schindler (29.10.1989–16.5.2020). The second author gratefully acknowledges the permission of his family to publish this paper posthumously.

Kilian Memory

Inauguration of the Kilian Schindler Excellence Award

Degree awarded posthumously to Dr. Killian Schindler

Abstract

This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behavior) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value.