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Nelin. Dinam., 2015, Volume 11, Number 4, Pages 735–762 (Mi nd505)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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


Full text: PDF file (492 kB)
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English version:
International Journal of Bifurcation and Chaos, 2015, 25:10, 15300–21

Bibliographic databases:

Document Type: Article
UDC: 517.925, 517.938.5, 531.396
MSC: 70F25, 37J60, 37J05
Received: 27.01.2015
Revised: 29.04.2015

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
\Bibitem{BizBolBor15}
\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}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000361916800004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84942744450}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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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