Effect of collision duration on the chaotic dynamics of a ball bouncing on a vertically vibrating plate

Abstract

Experiments have been performed to study the chaotic dynamics of a ball bouncing on a vertically vibrating plate. The velocity dependence of collision duration and coefficient of restitution is determined, and phase portraits of chaotic structures for the flight time and the relative collision velocities are obtained. Numerical calculations are carried out to examine the effects of velocity-dependent collision duration on the ball dynamics. It is revealed that when the collision is instantaneous, sticking solutions are always observed, whereas when the collision duration is taken into account, sticking solutions are destroyed and thereby chaos behaviors are induced.