Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2015, Volume 11, Number 4, Pages 763–823 (Mi nd507)  
This article is cited in 42 scientific papers (total in 42 papers)

Translated papers

Symmetries and reduction in nonholonomic mechanics

A. V. Borisov, I. S. Mamaev

Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia
Full-text PDF (909 kB) Citations (42)
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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
Ministry of Education and Science of the Russian Federation
Received: 01.08.2015
Revised: 10.09.2015
English version:
Regul. Chaotic Dyn., 2015, Volume 20, Issue 5, Pages 553–604
DOI: https://doi.org/10.1134/S1560354715050044
Document Type: Article
UDC: 517.925
MSC: 37J60, 37J35, 37C10
Language: Russian
Citation: A. V. Borisov, I. S. Mamaev, “Symmetries and reduction in nonholonomic mechanics”, Nelin. Dinam., 11:4 (2015), 763–823; Regul. Chaotic Dyn., 20:5 (2015), 553–604
Citation in format AMSBIB
\Bibitem{BorMam15}
\by A.~V.~Borisov, I.~S.~Mamaev
\paper Symmetries and reduction in nonholonomic mechanics
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 4
\pages 763--823
\mathnet{http://mi.mathnet.ru/nd507}
\transl
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 5
\pages 553--604
\crossref{https://doi.org/10.1134/S1560354715050044}
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  • https://www.mathnet.ru/eng/nd/v11/i4/p763
    Translation
    This publication is cited in the following 42 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Нелинейная динамика
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