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Regular and Chaotic Dynamics, 2006, Volume 11, Issue 4, Pages 455–466
DOI: https://doi.org/10.1070/RD2006v011n04ABEH000363 (Mi rcd686) 		 
This article is cited in 19 scientific papers (total in 19 papers)

On the problem of motion of vortex sources on a plane

A. V. Borisov, I. S. Mamaev

Institute of Computer Science, Udmurt State University, 1, Universitetskaya Str., Izhevsk 426034, Russia
Citations (19)
DOI: https://doi.org/10.1070/RD2006v011n04ABEH000363
Abstract: Equations of motion of vortex sources (examined earlier by Fridman and Polubarinova) are studied, and the problems of their being Hamiltonian and integrable are discussed. A system of two vortex sources and three sources-sinks was examined. Their behavior was found to be regular. Qualitative analysis of this system was made, and the class of Liouville integrable systems is considered. Particular solutions analogous to the homothetic configurations in celestial mechanics are given.
Keywords: vortex sources, integrability, Hamiltonian, point vortex.
Received: 05.09.2005
Revised: 07.03.2006
Bibliographic databases:
Document Type: Article
MSC: 37N05, 76M23
Language: English
Citation: A. V. Borisov, I. S. Mamaev, “On the problem of motion of vortex sources on a plane”, Regul. Chaotic Dyn., 11:4 (2006), 455–466
Citation in format AMSBIB
\Bibitem{BorMam06}
\by A. V. Borisov, I. S. Mamaev
\paper On the problem of motion of vortex sources on a plane
\jour Regul. Chaotic Dyn.
\yr 2006
\vol 11
\issue 4
\pages 455--466
\mathnet{http://mi.mathnet.ru/rcd686}
\crossref{https://doi.org/10.1070/RD2006v011n04ABEH000363}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2292204}
\zmath{https://zbmath.org/?q=an:1164.37353}
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    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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