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Regular and Chaotic Dynamics, 2015, Volume 20, Issue 3, Pages 383–400
DOI: https://doi.org/10.1134/S1560354715030107 (Mi rcd2) 		 
This article is cited in 41 scientific papers (total in 41 papers)

The Jacobi Integral in Nonholonomic Mechanics

A. V. Borisovab, I. S. Mamaevac, I. A. Bizyaevad

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia
b Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700, Russia
c M. T. Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069, Russia
d Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia
Citations (41)
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DOI: https://doi.org/10.1134/S1560354715030107
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
Russian Science Foundation 14-50-00005
This work was supported by the Russian Scientific Foundation (project 14-50-00005) and was carried out at the Steklov Mathematical Institute of the Russian Academy of Sciences.
Received: 28.04.2015
Accepted: 13.05.2015
Bibliographic databases:
Document Type: Article
MSC: 70F25, 37J60, 70E18
Language: English
Citation: A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “The Jacobi Integral in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:3 (2015), 383–400
Citation in format AMSBIB
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\by A.~V.~Borisov, I.~S.~Mamaev, I.~A.~Bizyaev
\paper The Jacobi Integral in Nonholonomic Mechanics
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 383--400
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