Fermi-like acceleration and power-law energy growth in nonholonomic systems

This paper is concerned with a nonholonomic system with parametric excitation—the Chaplygin sleigh with time-varying mass distribution. A detailed analysis is made of the problem of the existence of regimes with unbounded growth of energy (an analogue of Fermi's acceleration) in the case where excitation is achieved by means of a rotor with variable angular momentum. The existence of trajectories for which the translational velocity of the sleigh increases indefinitely and has the asymptotics is proved. In addition, it is shown that, when viscous friction with a nondegenerate Rayleigh function is added, unbounded speed-up disappears and the trajectories of the reduced system asymptotically tend to a limit cycle.