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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 Béghin’s 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 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
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English version:
Regular and Chaotic Dinamics, 2015, 20:3, 205–224
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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http://mi.mathnet.ru/eng/nd485 http://mi.mathnet.ru/eng/nd/v11/i2/p353
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This publication is cited in the following articles:
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V. V. Kozlov, “The dynamics of systems with servoconstraints. II”, Regular and Chaotic Dinamics, 20:4 (2015), 401–427
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V. P. Pavlov, V. M. Sergeev, “Fluid dynamics and thermodynamics as a unified field theory”, Proc. Steklov Inst. Math., 294 (2016), 222–232
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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
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