Chaotic dynamics of an air-damped bouncing ball.

A ball bouncing elastically upon a vertically vibrated platform is one of the simplest examples of a chaotic system. If dissipation is introduced at each bounce through a coefficient of restitution, the motion is no longer chaotic; the trajectories exhibit locking solutions that result in periodic behavior. Here we investigate the dynamics of a bouncing ball influenced by air damping. We consider the effects of both static air and air moving with the platform, and show that there is an exact mapping between them. In either case, the system has a rather complex dynamical behavior including truly chaotic trajectories. Our results highlight the importance of air effects for fine particulate systems.