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Sibirsk. Mat. Zh., 2007, Volume 48, Number 1, Pages 33–45 (Mi smj4)  

This article is cited in 35 scientific papers (total in 35 papers)

Isomorphism and Hamilton representation of some nonholonomic systems

A. V. Borisovab, I. S. Mamaevab

a Udmurt State University
b Institute of Computer Science

Abstract: We consider some questions connected with the Hamiltonian form of the two problems of nonholonomic mechanics: the Chaplygin ball problem and the Veselova problem. For these problems we find representations in the form of the generalized Chaplygin systems that can be integrated by the reducing multiplier method. We give a concrete algebraic form of the Poisson brackets which, together with an appropriate change of time, enable us to write down the equations of motion of the problems under study. Some generalization of these problems are considered and new ways of implementation of nonholonomic constraints are proposed. We list a series of nonholonomic systems possessing an invariant measure and sufficiently many first integrals for which the question about the Hamiltonian form remains open even after change of time. We prove a theorem on isomorphism of the dynamics of the Chaplygin ball and the motion of a body in a fluid in the Clebsch case.

Keywords: nonholonomic system, reducing multiplier, Hamiltonization, isomorphism.

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English version:
Siberian Mathematical Journal, 2007, 48:1, 26–36

Bibliographic databases:

UDC: 531.38
Received: 04.07.2005

Citation: A. V. Borisov, I. S. Mamaev, “Isomorphism and Hamilton representation of some nonholonomic systems”, Sibirsk. Mat. Zh., 48:1 (2007), 33–45; Siberian Math. J., 48:1 (2007), 26–36

Citation in format AMSBIB
\by A.~V.~Borisov, I.~S.~Mamaev
\paper Isomorphism and Hamilton representation of some nonholonomic systems
\jour Sibirsk. Mat. Zh.
\yr 2007
\vol 48
\issue 1
\pages 33--45
\jour Siberian Math. J.
\yr 2007
\vol 48
\issue 1
\pages 26--36

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    This publication is cited in the following articles:
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    3. Borisov A.V., Mamaev I.S., Marikhin V.G., “Explicit Integration of One Problem in Nonholonomic Mechanics”, Dokl. Phys., 53:10 (2008), 525–528  mathnet  crossref  mathscinet  zmath  zmath  adsnasa  isi  elib  elib  scopus
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