Chaotic dynamics of a bouncing ball – Numerical and experimental investigations

Abstract

We demonstrate the chaotic dynamics of a simple dissipative dynamical system consisting of a bouncing ball subject to repeated impacts with a sinusoidally-oscillating plate. At low driving frequencies, the ball after a few inelastic bounces eventually sticks and moves with the plate. However, as the driving frequency is increased, the ball bounces with a period exactly equal to the driving period. The experimental and numerical results show that with further increase in the driving frequency, the ball exhibits series of period-doubling cascades which is an indicative measure of the onset of chaos. The experimental investigation employed the Vision-Based Motion Sensor developed in USC and the results were compared with the numerical solution.