Dynamics of the Chaplygin Ball with Variable Parameters

Abstract

This work is devoted to the study of the dynamics of the Chaplygin ball with variable moments of inertia, which occur due to the motion of pairs of internal material points, and internal rotors. The components of the inertia tensor and the gyrostatic momentum are periodic functions. In general, the problem is nonintegrable. In a special case, the relationship of the problem under consideration with the Liouville problem with changing parameters is shown. The case of the Chaplygin ball moving from rest is considered separately. Poincaré maps are constructed, strange attractors are found, and the stages of the origin of strange attractors are shown. Also, the trajectories of contact points are constructed to confirm the chaotic dynamics of the ball. A chart of dynamical regimes is constructed in a separate case for analyzing the nature of strange attractors.

Motion Control of a Spherical Robot with a Pendulum Actuator for Pursuing a Target

“…A spherical robot is a spherical shell which rolls without slipping and at the center of which an axisymmetric pendulum equipped with a pendulum actuator is installed. The problem of a spherical shell rolling without slipping is a classical nonholonomic problem which has received a fair share of attention in the literature, for example, in [5][6][7][8][9][10][11][12][13]. There are also papers devoted to the problem of controlling the rolling motion using rotors and gyrostats [14][15][16][17].…”