Dynamics of Chaplygin skate on a horizontal plane with dry anisotropic friction

The problem of Chaplygin's skate motion on the horizontal plane with dry friction is considered. It is supposed that the friction force depends on an angle between the sliding velocity and the skate plane. It is shown that the time of the skate sliding is defined by a transcendental equation and depends on the initial values of the angular velocity, the sliding velocity and the angle between the sliding velocity and the skate plane. The countable set of initial values of the sliding velocity such that the sliding time does not depend on this angle is found.