The Phenomenon of Reversal in the Euler–Poincaré–Suslov Nonholonomic Systems

Abstract

The development of robotics makes it necessary to study the problem of controlling nonholonomic systems (Svinin et al., Regul Chaotic Dyn. 2013; 18(1---2): 126---143, Borisov et al., Regul. Chaotic Dyn. 2013; 18(1---2): 144---158, Ivanova et al., Regul Chaotic Dyn. 2014; 19(1): 140---143). In this paper, the dynamics of nonholonomic systems on Lie groups with a left-invariant kinetic energy and left-invariant constraints are considered. Equations of motion form a closed system of differential equations on the corresponding Lie algebra. In addition, the effect of change in the stability of steady motions of these systems with the direction of motion reversed (the reversal found in rattleback dynamics) is discussed. As an illustration, the rotation of a rigid body with a fixed point and the Suslov nonholonomic constraint as well as the motion of the Chaplygin sleigh is considered.