Dynamics of a ball bouncing on a rough inclined line

Abstract

We present here a simple theoretical model that describes the motion of ball bouncing on a rough inclined line. The rough line consists of microfacets whose orientation can be different from the line inclination. We examine the behavior of the ball as a function of the orientation of the microfacets and determine the conditions under which the jumps of the ball are decreasing or increasing in their amplitude. In particular we show that when the facet inclination varies along the line with a well-defined spatial periodicity the ball can reach a steady bouncing regime that leads ultimately to chaotic behavior via a period-doubling scenario. Furthermore, we find that the presence of noise associated with facet inclination destroys the structure of the chaotic regime.