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Nelin. Dinam., 2015, Volume 11, Number 4, Pages 763–823 (Mi nd507)  

Translated papers

Symmetries and reduction in nonholonomic mechanics

A. V. Borisov, I. S. Mamaev

Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia

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


Full text: PDF file (909 kB)
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English version:
Regul. Chaotic Dyn., 2015, 20:5, 553–604

Document Type: Article
UDC: 517.925
MSC: 37J60, 37J35, 37C10
Received: 01.08.2015
Revised: 10.09.2015

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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    Translation
  • Нелинейная динамика
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