Spinning rough disk moving in a rarefied medium

A spinning rough disk moves through a rarefied medium on the plane. The roughness is formed by small cavities on the disk boundary. The medium is so rare that mutual interaction of particles can be neglected. All collisions of particles with the disk are perfectly elastic; there may happen multiple collisions in the cavities. We calculate the force of resistance acting on the body and examine how it depends on the kind of roughness (shape of the cavities). We show that the nonzero transversal component of the force generally appears, resulting in deflection of the disk trajectory. In several simple cases the trajectory is determined. We compare our results with the ones known in the literature. It is known that there is a transversal force acting on a spinning body (most often a sphere or a cylinder) moving in a rarefied gas, due to nonelastic interaction of gas particles with the body. We propose another mechanism of creating the transversal force, resulting from multiple reflections of particles from the body. Mathematics subject classifications: