Bouncing ball dynamics: simple model of motion of the table and sinusoidal motion

Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincar'e map, describing evolution from an impact to the next impact, is described. Displacement of the table is approximated in one period by four cubic polynomials. Results obtained for this model are used to elucidate dynamics of the standard model of bouncing ball with sinusoidal motion of the limiter.