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Nelin. Dinam., 2010, Volume 6, Number 1, Pages 127–142 (Mi nd60)  

This article is cited in 5 scientific papers (total in 5 papers)

Hamiltonian representation and integrability of the Suslov problem

A. V. Borisov, A. A. Kilin, I. S. Mamaev

Institute of Computer Science

Abstract: We consider the problems of Hamiltonian representation and integrability of the nonholonomic Suslov system and its generalization suggested by S. A. Chaplygin. These aspects are very important for understanding the dynamics and qualitative analysis of the system. In particular, they are related to the nontrivial asymptotic behaviour (i.e. to some scattering problem). The paper presents a general approach based on the study of the hierarchy of dynamical behaviour of nonholonomic systems.

Keywords: Hamiltonian system, Poisson bracket, nonholonomic constraint, invariant measure, integrability.

Full text: PDF file (654 kB)
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Document Type: Article
UDC: 531.38
MSC: 34D20, 70E40, 37J35
Received: 11.11.2009

Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Hamiltonian representation and integrability of the Suslov problem”, Nelin. Dinam., 6:1 (2010), 127–142

Citation in format AMSBIB
\Bibitem{BorKilMam10}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Hamiltonian representation and integrability of the Suslov problem
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 1
\pages 127--142
\mathnet{http://mi.mathnet.ru/nd60}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    2. A. Yu. Konyaev, “Classification of Lie algebras with generic orbits of dimension 2 in the coadjoint representation”, Sb. Math., 205:1 (2014), 45–62  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “On the Nonlinear Poisson Bracket Arising in Nonholonomic Mechanics”, Math. Notes, 95:3 (2014), 308–315  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. I. A. Bizyaev, V. V. Kozlov, “Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method”, Sb. Math., 206:12 (2015), 1682–1706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. I. A. Bizyaev, A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and bifurcations in nonholonomic mechanics”, 25, no. 10, 2015, 15300–21  mathnet  crossref  isi
  • Нелинейная динамика
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