Modelling of the motion of a disk rolling on a torus

This work deals with the modelling of the motion of a disk rolling without slipping on a rigid torus. It is assumed here that the motion of the disk is controlled by a tilting moment, a directional moment, and a pedalling moment. A mathematical model of the motion of the disk rolling on the torus is derived. Then, it is shown that an inverse control transformation can be applied to linearize the system.