Two balls in one dimension with gravity

A study is reported of a simple dynamical system with two degrees of freedom having discontinuities due to collisions. It consists of two point masses or balls constrained to move in one dimension above a floor in a constant gravitational field. All collisions are assumed to be elastic. When the ratio r of the upper mass to the lower mass is less than unity the motion is chaotic almost everywhere. On the other hand, when r>1 the motion shows …