Dynamical properties of granular rotors

Abstract

The stochastic motion of an arbitrarily shaped rotor, free to rotate around a fixed axis as a result of dissipative collisions with a surrounding thermalized gas, is investigated. A Boltzmann master equation is derived, starting from the elementary gas–rotor collisions. Analytical expressions for the moments of the rotational speed and the rotational temperature are obtained in the form of a series expansion, using the mass ratio of the gas particle and the rotor as the expansion parameter. We discuss the general features of the motion, which is largely determined by the geometry of the rotor. In particular, a stationary non-zero rotation is observed for rotationally asymmetric rotors. Molecular dynamics simulations support the analytical results.