Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2015, Volume 11, Number 2, Pages 377–396 (Mi nd486)  
This article is cited in 34 scientific papers (total in 34 papers)

Translated papers

The Jacobi integral in nonholonomic mechanics

A. V. Borisova, I. S. Mamaeva, I. A. Bizyaevb

a Moscow Institute of Physics and Technology (State University) 9 Institutskiy per., Dolgoprudny, Moscow, 141700, Russia
b Udmurt State University Universitetskaya 1, Izhevsk, 426034, Russia
Full-text PDF (1935 kB) Citations (34)
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Abstract: In this paper we discuss conditions for the existence of the Jacobi integral (that generalizes energy) in systems with inhomogeneous and nonholonomic constraints. As an example, we consider in detail the problem of motion of the Chaplygin sleigh on a rotating plane and the motion of a dynamically symmetric ball on a uniformly rotating surface. In addition, we discuss illustrative mechanical models based on the motion of a homogeneous ball on a rotating table and on the Beltrami surface.
Keywords: nonholonomic constraint, Jacobi integral, Chaplygin sleigh, rotating table, Suslov problem.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 15-38-20879 мол_а_вед
Received: 28.04.2015
Revised: 13.05.2015
English version:
Regul. Chaotic Dyn., 2015, Volume 20, Issue 3, Pages 383–400
DOI: https://doi.org/10.1134/S1560354715030107
Document Type: Article
UDC: 531.384, 517.925
MSC: 70F25, 37J60, 70E18
Language: Russian
Citation: A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “The Jacobi integral in nonholonomic mechanics”, Nelin. Dinam., 11:2 (2015), 377–396; Regul. Chaotic Dyn., 20:3 (2015), 383–400
Citation in format AMSBIB
\Bibitem{BorMamBiz15}
\by A.~V.~Borisov, I.~S.~Mamaev, I.~A.~Bizyaev
\paper The Jacobi integral in nonholonomic mechanics
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 2
\pages 377--396
\mathnet{http://mi.mathnet.ru/nd486}
\transl
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 383--400
\crossref{https://doi.org/10.1134/S1560354715030107}
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  • https://www.mathnet.ru/eng/nd/v11/i2/p377
    Translation
    This publication is cited in the following 34 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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