Dynamics of a spherical robot with periodically changing moments of inertia

The motion of a spherical robot with periodically changing moments of inertia and gyrostatic momentum is considered. Equations of motion are derived within the framework of the model of "rubber" rolling (without slipping and twisting). The stability of partial solutions of the system is studied numerically. It is shown that the system is nonconservative, and, as a consequence, limit cycles and strange attractors exist in the phase space of the system.