NONLINEAR DYNAMICS OF A BOUNCING BALL DRIVEN BY ELECTRIC FORCES

Abstract

This paper is devoted to a theoretical and experimental study of the dynamics of a bouncing ball driven by an electric force. The experimental model consists of a metallic ball immersed in a poorly conducting liquid between two horizontal electrodes. The ball bounces upon the lower electrode as a high voltage is applied between the two plates. The measurement of the time between successive impacts produces a time series, which depends on two control parameters, the amplitude and the frequency of the applied voltage. A theoretical model is proposed, which provides a discrete nonlinear map, and discussed in comparison with the experimental results. It is shown that the system exhibits a period doubling route to chaos and a non-Feigenbaum universal scaling at the onset of chaos. Chaotic motion is investigated using the usual tools: Lyapunov exponents, correlation dimensions and entropies. Fractal structure of the chaotic attractor is also brought to evidence in experimental time series as well as in numerical simulations.