Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2015, Volume 11, Number 4, Pages 735–762 (Mi nd505)  
This article is cited in 12 scientific papers (total in 12 papers)

Translated papers

Topology and bifurcations in nonholonomic mechanics

I. A. Bizyaeva, A. V. Bolsinovb, A. V. Borisova, I. S. Mamaeva

a Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia
b School of Mathematics, Loughborough University, United Kingdom, LE11 3TU, Loughborough, Leicestershire
Full-text PDF (492 kB) Citations (12)
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Abstract: This paper develops topological methods for qualitative analysis of the behavior of nonholonomic dynamical systems. Their application is illustrated by considering a new integrable system of nonholonomic mechanics, called a nonholonomic hinge. Although this system is nonholonomic, it can be represented in Hamiltonian form with a Lie–Poisson bracket of rank 2. This Lie–Poisson bracket is used to perform stability analysis of fixed points. In addition, all possible types of integral manifolds are found and a classification of trajectories on them is presented.
Keywords: nonholonomic hinge, topology, bifurcation diagram, tensor invariants, Poisson bracket, stability.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Received: 27.01.2015
Revised: 29.04.2015
English version:
International Journal of Bifurcation and Chaos, 2015, Volume 25, Issue 10, Pages 15300–21
DOI: https://doi.org/10.1142/S0218127415300281
Bibliographic databases:
Document Type: Article
UDC: 517.925, 517.938.5, 531.396
MSC: 70F25, 37J60, 37J05
Language: Russian
Citation: I. A. Bizyaev, A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and bifurcations in nonholonomic mechanics”, Nelin. Dinam., 11:4 (2015), 735–762; International Journal of Bifurcation and Chaos, 25:10 (2015), 15300–21
Citation in format AMSBIB
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\by I.~A.~Bizyaev, A.~V.~Bolsinov, A.~V.~Borisov, I.~S.~Mamaev
\paper Topology and bifurcations in nonholonomic mechanics
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 4
\pages 735--762
\mathnet{http://mi.mathnet.ru/nd505}
\transl
\jour International Journal of Bifurcation and Chaos
\yr 2015
\vol 25
\issue 10
\pages 15300--21
\crossref{https://doi.org/10.1142/S0218127415300281}
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  • https://www.mathnet.ru/eng/nd/v11/i4/p735
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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