This article is cited in 18 scientific papers (total in 18 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
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.
reduction, symmetry, tensor invariant, first integral, symmetry group, symmetry field, nonholonomic constraint, Noether theorem
|Russian Science Foundation
|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.
MSC: 37J60, 37J35, 37C10
Alexey V. Borisov, Ivan S. Mamaev, “Symmetries and Reduction in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:5 (2015), 553–604
Citation in format AMSBIB
\by Alexey V. Borisov, Ivan S. Mamaev
\paper Symmetries and Reduction in Nonholonomic Mechanics
\jour Regul. Chaotic Dyn.
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Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Hess–Appelrot Case and Quantization of the Rotation Number”, Regul. Chaotic Dyn., 22:2 (2017), 180–196
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S. P. Kuznetsov, “Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint”, EPL, 118:1 (2017), 10007
L. C. Garcia-Naranjo, J. Montaldi, “Gauge momenta as Casimir functions of nonholonomic systems”, Arch. Ration. Mech. Anal., 228:2 (2018), 563–602
Sergey P. Kuznetsov, “Regular and Chaotic Dynamics of a Chaplygin Sleigh due to Periodic Switch of the Nonholonomic Constraint”, Regul. Chaotic Dyn., 23:2 (2018), 178–192
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