An analytical and numerical study of chaotic dynamics in a simple bouncing ball model

Dynamics of a ball moving in gravitational field and colliding with a moving table is studied in this paper. The motion of the limiter is assumed as periodic with piecewise constant velocity—it is assumed that the table moves up with a constant velocity and then moves down with another constant velocity. The Poincaré map, describing evolution from an impact to the next impact, is derived and scenarios of transition to chaotic dynamics are investigated analytically and numerically.