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Nelin. Dinam., 2014, Volume 10, Number 1, Pages 59–72 (Mi nd425)  

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

Falling Motion of a circular cylinder interacting dynamically with $N$ point vortices

Sergey V. Sokolov

Institute of Computer Science, Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia

Abstract: The dynamical behavior of a heavy circular cylinder and $N$ point vortices in an unbounded volume of ideal liquid is considered. The liquid is assumed to be irrotational and at rest at infinity. The circulation about the cylinder is different from zero. The governing equations are presented in Hamiltonian form. Integrals of motion are found. Allowable types of trajectories are discussed in the case $N = 1$. The stability of finding equilibrium solutions is investigated and some remarkable types of partial solutions of the system are presented. Poincaré sections of the system demonstrate chaotic behavior of dynamics, which indicates a non-integrability of the system.

Keywords: point vortices, Hamiltonian systems, reduction, stability of equilibrium solutions.

Full text: PDF file (467 kB)
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Document Type: Article
UDC: 512.77, 517.912
MSC: 70Hxx, 70G65
Received: 10.01.2014
Revised: 28.01.2014

Citation: Sergey V. Sokolov, “Falling Motion of a circular cylinder interacting dynamically with $N$ point vortices”, Nelin. Dinam., 10:1 (2014), 59–72

Citation in format AMSBIB
\Bibitem{Sok14}
\by Sergey~V.~Sokolov
\paper Falling Motion of a circular cylinder interacting dynamically with $N$ point vortices
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 1
\pages 59--72
\mathnet{http://mi.mathnet.ru/nd425}


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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. S. V. Sokolov, “Dvizhenie krugovogo tsilindra, vzaimodeistvuyuschego s vikhrevoi paroi, v pole sily tyazhesti v idealnoi zhidkosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 86–99  mathnet
    2. S. V. Sokolov, I. S. Koltsov, “Khaoticheskoe rasseyanie tochechnogo vikhrya krugovym tsilindricheskim tverdym telom, dvizhuschimsya v pole tyazhesti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:2 (2015), 184–196  mathnet  elib
  • Нелинейная динамика
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