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Regular and Chaotic Dynamics, 2015, Volume 20, Issue 5, Pages 553–604
DOI: https://doi.org/10.1134/S1560354715050044 (Mi rcd21) 		 
This article is cited in 52 scientific papers (total in 52 papers)

Symmetries and Reduction in Nonholonomic Mechanics

Alexey V. Borisova, Ivan S. Mamaevb

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b M. T. Kalashnikov Izhevsk State Technical University ul. Studencheskaya 7, Izhevsk, 426069 Russia
Citations (52)
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DOI: https://doi.org/10.1134/S1560354715050044
Abstract: This paper is a review of the problem of the constructive reduction of nonholonomic systems with symmetries. The connection of reduction with the presence of the simplest tensor invariants (first integrals and symmetry fields) is shown. All theoretical constructions are illustrated by examples encountered in applications. In addition, the paper contains a short historical and critical sketch covering the contribution of various researchers to this problem.
Keywords: reduction, symmetry, tensor invariant, first integral, symmetry group, symmetry field, nonholonomic constraint, Noether theorem.
Funding agency Grant number
Russian Science Foundation 15-12-20035
14-19-01303
Sections 2-4 were written by A. V. Borisov and supported by the RSF grant no. 15-12-20035. Sections 5, 6 and Appendices were written by I. S. Mamaev within the framework of the RSF grant no. 14-19-01303.
Received: 01.08.2015
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37J35, 37C10
Language: English
Citation: Alexey V. Borisov, Ivan S. Mamaev, “Symmetries and Reduction in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:5 (2015), 553–604
Citation in format AMSBIB
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\by Alexey V. Borisov, Ivan S. Mamaev
\paper Symmetries and Reduction in Nonholonomic Mechanics
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 5
\pages 553--604
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    This publication is cited in the following 52 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:69
     
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