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 Regul. Chaotic Dyn., 2015, Volume 20, Issue 3, Pages 205–224 (Mi rcd1)

The Dynamics of Systems with Servoconstraints. I

Valery V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

Abstract: The paper discusses the dynamics of systems with Béghin's servoconstraints where the constraints are realized by means of controlled forces. Classical nonholonomic systems are an important particular case. Special attention is given to the study of motion on Lie groups with left-invariant kinetic energy and left-invariant constraints. The presence of symmetries allows one to reduce the dynamic equations to a closed system of differential equations with quadratic right-hand sides on a Lie algebra. Examples are given which include the rotation of a rigid body with a left-invariant servoconstraint — the projection of the angular velocity onto some direction fixed in the body is equal to zero (a generalization of the nonholonomic Suslov problem) — and the motion of the Chaplygin sleigh with servoconstraints of a certain type. The dynamics of systems with Béghin's servoconstraints is richer and more varied than the more usual dynamics of nonholonomic systems.

Keywords: servoconstraints, symmetries, Lie groups, left-invariant constraints, systems with quadratic right-hand sides.

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 The study was financed by the grant from the Russian Science Foundation (Project No. 14-5000005).

DOI: https://doi.org/10.1134/S1560354715030016

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MSC: 34D20, 70F25, 70Q05
Accepted:05.03.2015
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Citation: Valery V. Kozlov, “The Dynamics of Systems with Servoconstraints. I”, Regul. Chaotic Dyn., 20:3 (2015), 205–224

Citation in format AMSBIB
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This publication is cited in the following articles:
1. Valery V. Kozlov, “The Dynamics of Systems with Servoconstraints. II”, Regul. Chaotic Dyn., 20:4 (2015), 401–427
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