Dynamic analysis of a ball bouncing on a flexible beam

In this work we investigate the problem of a ball repeatedly bouncing on a flexible beam with hinged-hinged boundary conditions. A simple model for the impact is proposed, which allows to determine the velocity of the ball and of the beam out of the impact given the entering velocities. Several simulations are reported aimed at illustrating various aspects of the nonlinear dynamics of the considered system, including ball motion reversal, chaotic motion, chattering, etc. A lot of attention is paid to the sensitive dependence on initial conditions and on small changes in the system parameters, which seems to be the most important dynamical behaviour. The effects of the initial velocity of the ball, and on the ball-to-beam mass ratio are investigated, too.