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Journal of Dynamical and Control Systems
Published in: Journal of Dynamical and Control Systems 4/2016

09-11-2015

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

Author: Valery Kozlov

Published in: Journal of Dynamical and Control Systems | Issue 4/2016

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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.
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Metadata
Title
The Phenomenon of Reversal in the Euler–Poincaré–Suslov Nonholonomic Systems
Author
Valery Kozlov
Publication date
09-11-2015
Publisher
Springer US
Published in
Journal of Dynamical and Control Systems / Issue 4/2016
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-015-9305-4

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