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Nelin. Dinam., 2014, Volume 10, Number 1, Pages 101–112 (Mi nd427)  

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

Focus-focus singularities in classical mechanics

Gleb E. Smirnov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Leninskye gori 1, GSP-1, Moscow, 119991, Russia

Abstract: In this paper the local singularities of integrable Hamiltonian systems with two degrees of freedom are studied. The topological obstruction to the existence of a focus-focus singularity with given complexity is found. It is shown that only simple focus-focus singularities can appear in a typical mechanical system. Model examples of mechanical systems with complicated focus-focus singularity are given.

Keywords: integrable hamiltonian systems, focus-focus singularities, obstruction to the existence of singularities.

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Document Type: Article
UDC: 517.938.5
MSC: 37J35
Received: 08.12.2013
Revised: 25.02.2014

Citation: Gleb E. Smirnov, “Focus-focus singularities in classical mechanics”, Nelin. Dinam., 10:1 (2014), 101–112

Citation in format AMSBIB
\Bibitem{Smi14}
\by Gleb~E.~Smirnov
\paper Focus-focus singularities in classical mechanics
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 1
\pages 101--112
\mathnet{http://mi.mathnet.ru/nd427}


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    This publication is cited in the following articles:
    1. A. V. Bolsinov, “Complete commutative subalgebras in polynomial Poisson algebras: a proof of the Mischenko-Fomenko conjecture”, Theor. Appl. Mech., 43:2 (2016), 145–168  crossref  isi
  • Нелинейная динамика
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