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Nelin. Dinam., 2013, Volume 9, Number 2, Pages 203–227 (Mi nd386)  

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

Topological monodromy in nonholonomic systems

Alexey V. Bolsinovab, Alexander A. Kilinb, Alexey O. Kazakovb

a School of Mathematics, Loughborough University, United Kingdom, LE11 3TU, Loughborough, Leicestershire
b Institute of Computer Science; Laboratory of nonlinear analysis and the design of new types of vehicles, Udmurt State University, Izhevsk, Russia

Abstract: The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no difference between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane.

Keywords: topological monodromy, integrable systems, nonholonomic systems, Poincaré map, bifurcation analysis, focus-focus singularities.

Full text: PDF file (1771 kB)
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Document Type: Article
UDC: 517.925+517.938.5
MSC: 37J05, 34C14
Received: 28.03.2013
Revised: 13.05.2013

Citation: Alexey V. Bolsinov, Alexander A. Kilin, Alexey O. Kazakov, “Topological monodromy in nonholonomic systems”, Nelin. Dinam., 9:2 (2013), 203–227

Citation in format AMSBIB
\Bibitem{BolKilKaz13}
\by Alexey~V.~Bolsinov, Alexander~A.~Kilin, Alexey~O.~Kazakov
\paper Topological monodromy in nonholonomic systems
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 2
\pages 203--227
\mathnet{http://mi.mathnet.ru/nd386}


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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. G. E. Smirnov, “Fokusnye osobennosti v klassicheskoi mekhanike”, Nelineinaya dinam., 10:1 (2014), 101–112  mathnet
    2. A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Нелинейная динамика
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