Dynamics of a Chaplygin sleigh with an unbalanced rotor: regular and chaotic motions

This paper addresses the problem of the motion of a sleigh with a free rotor. It is shown that this system exhibits chaotic and regular motions. The case in which the system is balanced relative to the knife edge is of particular interest because it has an additional integral. In this case, the problem reduces to investigating a vector field on a torus and to classifying singular points on it.