Motion of a Rough Disc in Newtonian Aerodynamics

Dynamics of a rough disc in a rarefied medium is considered. We prove that any finite rectifiable curve can be approximated in the Hausdorff metric by trajectories of centers of rough discs provided that the parameters of the system are carefully chosen. To control the dynamics of the disc, we use the so-called inverse Magnus effect which causes deviation of the trajectory of a spinning body. We study the so-called response laws for scattering billiards e.g. relationship between the velocity of incidence of a particle and that of reflection. We construct a special family of such laws that is weakly dense in the set of symmetric Borel measures. Then we find a shape of cavities that provides selected law of reflections. We write down differential equations that describe motions of rough discs. We demonstrate how a given curve can be approximated by considered trajectories.