Chaotic dynamics in a simple bouncing ball model

Abstract

We study dynamics of a ball moving in gravitational field and colliding with a moving table. 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 Poincare map, describing evolution from an impact to the next impact, is derived and scenarios of transition to chaotic dynamics are investigated analytically.

LaTeX, 11 pages, 7 figures

References in corpus (2)

• Chaotic dynamics in a simple bouncing ball model
• Grazing dynamics and dependence on initial conditions in certain systems with impacts

Cited by in corpus (7)

• Bouncing ball dynamics: simple model of motion of the table and sinusoidal motion
• Chaotic dynamics in a simple bouncing ball model
• Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time
• Geometrical origin of chaoticity in the bouncing ball billiard
• Simple model of bouncing ball dynamics. Displacement of the limiter assumed as a cubic function of time
• Simple models of bouncing ball dynamics and their comparison
• Local bifurcation structure of a bouncing ball system with a piecewise polynomial function for table displacement