  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.
