Fly-wheel model exhibits the hither and thither motion of a bouncing ball

The to and fro motion of a bouncing ball on a flat surface is represented by a low-dimensional model. To describe the repeated reversals of the horizontal velocity of the ball, the elasticity of the ball has to be taken into account. We show that a simple fly-wheel model exhibits the observed hither and thither motion of elastic balls. The suggested model is capable of describing oblique impacts of spherical bodies, which can be important in many applications, including dynamical simulation of granular materials. We find that the behaviour of the bouncing fly-wheel is sensitive to the initial conditions, and the escape time plots are used to illustrate this observation.