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Regul. Chaotic Dyn., 2012, Volume 17, Issue 2, Pages 131–141 (Mi rcd266)  

This article is cited in 5 scientific papers (total in 5 papers)

On Invariant Manifolds of Nonholonomic Systems

Valery V. Kozlov

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

Abstract: Invariant manifolds of equations governing the dynamics of conservative nonholonomic systems are investigated. These manifolds are assumed to be uniquely projected onto configuration space. The invariance conditions are represented in the form of generalized Lamb’s equations. Conditions are found under which the solutions to these equations admit a hydrodynamical description typical of Hamiltonian systems. As an illustration, nonholonomic systems on Lie groups with a left-invariant metric and left-invariant (right-invariant) constraints are considered.

Keywords: invariant manifold, Lamb’s equation, vortex manifold, Bernoulli’s theorem, Helmholtz’ theorem.

DOI: https://doi.org/10.1134/S1560354712020037


Bibliographic databases:

MSC: 70Hxx, 37J60
Received: 27.12.2011
Accepted:23.01.2012
Language:

Citation: Valery V. Kozlov, “On Invariant Manifolds of Nonholonomic Systems”, Regul. Chaotic Dyn., 17:2 (2012), 131–141

Citation in format AMSBIB
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\by Valery V. Kozlov
\paper On Invariant Manifolds of Nonholonomic Systems
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 2
\pages 131--141
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\crossref{https://doi.org/10.1134/S1560354712020037}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202  mathnet
    2. A. V. Bolsinov, A. A. Kilin, A. O. Kazakov, “Topologicheskaya monodromiya v negolonomnykh sistemakh”, Nelineinaya dinam., 9:2 (2013), 203–227  mathnet
    3. Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere”, Regul. Chaotic Dyn., 18:3 (2013), 277–328  mathnet  crossref  mathscinet  zmath
    4. Valery V. Kozlov, “The Euler–Jacobi–Lie Integrability Theorem”, Regul. Chaotic Dyn., 18:4 (2013), 329–343  mathnet  crossref  mathscinet  zmath
    5. Bolsinov A.V. Kilin A.A. Kazakov A.O., “Topological Monodromy as An Obstruction to Hamiltonization of Nonholonomic Systems: Pro Or Contra?”, J. Geom. Phys., 87 (2015), 61–75  crossref  mathscinet  zmath  isi  scopus
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