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Nelin. Dinam., 2015, Volume 11, Number 2, Pages 377–396 (Mi nd486)  

This article is cited in 2 scientific papers (total in 2 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

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


Full text: PDF file (1935 kB)
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English version:
Regul. Chaotic Dyn., 2015, 20:3, 383–400

Document Type: Article
UDC: 531.384, 517.925
MSC: 70F25, 37J60, 70E18
Received: 28.04.2015
Revised: 13.05.2015

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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    Translation

    This publication is cited in the following articles:
    1. A. V. Borisov, I. S. Mamaev, “Symmetries and reduction in nonholonomic mechanics”, Regul. Chaotic Dyn., 20:5 (2015), 553–604  mathnet  crossref
    2. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Нелинейная динамика
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