Scattering of a classical rotating object by a screen with a slit

The scattering of a rod-like rotating object by a single slit on a screen is followed according to the laws of classical mechanics. We assume a free planar motion and a uniform rotation, except for the moments of collisions, causing discontinuous jumps in the velocity and the angular velocity of the object. The collisions, which are assumed to be ideally elastic, result in certain constrains and we show that the motion in the six-dimensional phase space of the problem can be mapped onto a 3D billiard. We simulate numerically the dynamics of the problem and find that the collision number shows a sensitive dependence on the initial conditions for certain regions of the phase space. This result forecasts the necessity of further caution in the quantum version of this problem, where entanglement of rotational and translational degrees of freedom should play a role. (paper)