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Nelin. Dinam., 2015, Volume 11, Number 2, Pages 353–376 (Mi nd485)  

This article is cited in 3 scientific papers (total in 3 papers)

Translated papers

The dynamics of systems with servoconstraints. I

V. V. Kozlov

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

Abstract: The paper discusses the dynamics of systems with Béghins servoconstraints wheretheconstraints 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 Béghins 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


Full text: PDF file (494 kB)
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English version:
Regular and Chaotic Dinamics, 2015, 20:3, 205–224

Document Type: Article
UDC: 531.36
MSC: 34D20, 70F25, 70Q05
Received: 10.02.2015
Revised: 05.03.2015

Citation: V. V. Kozlov, “The dynamics of systems with servoconstraints. I”, Nelin. Dinam., 11:2 (2015), 353–376; Regular and Chaotic Dinamics, 20:3 (2015), 205–224

Citation in format AMSBIB
\Bibitem{Koz15}
\by V.~V.~Kozlov
\paper The dynamics of systems with servoconstraints. I
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 2
\pages 353--376
\mathnet{http://mi.mathnet.ru/nd485}
\elib{http://elibrary.ru/item.asp?id=23828736}
\transl
\jour Regular and Chaotic Dinamics
\yr 2015
\vol 20
\issue 3
\pages 205--224
\crossref{https://doi.org/10.1134/S1560354715030016}


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    This publication is cited in the following articles:
    1. V. V. Kozlov, “The dynamics of systems with servoconstraints. II”, Regular and Chaotic Dinamics, 20:4 (2015), 401–427  mathnet  crossref
    2. V. P. Pavlov, V. M. Sergeev, “Fluid dynamics and thermodynamics as a unified field theory”, Proc. Steklov Inst. Math., 294 (2016), 222–232  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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