Horizontal stability of a bouncing ball

When a ball is released onto a vibrating flat surface, it will ultimately bounce periodically on the surface if the forcing amplitude is sufficiently small. In this work, we explore the dramatic effect that the inclusion of underlying surface topography can have on the observed motion of the ball. Particular focus is given to detailing the surprising manner in which a concave surface can actually destabilize purely vertical bouncing, such that horizontal motion naturally ensues. We show that the resulting motion can be periodic, quasi-periodic, or even chaotic and depends sensitively on the shape of the underlying surface.