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

Non-linear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered. The Poincaré map, describing evolution from an impact to the next impact, is used to analyse the original system. Sinusoidal displacement of the table, defining the standard model, is approximated in one period of the limiter׳s motion by a cubic spline, thus making analytical computations possible. Analytical and numerical results, based on Implicit Function Theorem, obtained for this simplified model, are used to elucidate dynamics of the standard model of the bouncing ball. Finally, the same techniques are applied to investigate dynamics of the standard model.