Climb of the Chaplygin Sleigh on an Inclined Plane under Periodic Controls: Speedup and Uniform Motion

This paper addresses the problem of the Chaplygin sleigh moving on an inclined plane under the action of periodic controls. Periodic controls are implemented by moving point masses. It is shown that, under periodic oscillations of one point mass in the direction perpendicular to that of the knife edge, for a nonzero initial velocity there exists a motion with acceleration or a uniform motion (on average per period) in the direction opposite to that of the largest descent. It is shown that adding to the system two point masses which move periodically along some circle enables a period-averaged uniform motion of the system from rest.