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Nelin. Dinam., 2014, Volume 10, Number 3, Pages 319–327 (Mi nd446)  

The dynamics of three vortex sources

Ivan A. Bizyaeva, Alexey V. Borisovab, Ivan S. Mamaevba

a Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia
b Institute of Mathematics and Mechanics of the Ural Branch of RAS, S. Kovalevskaja str. 16, Ekaterinburg, 620990, Russia

Abstract: In this paper, the integrability of the equations of a system of three vortex sources is shown. A reduced system describing, up to similarity, the evolution of the systems configurations is obtained. Possible phase portraits and various relative equilibria of the system are presented.

Keywords: integrability, vortex sources, shape sphere, reduction, homothetic configurations.

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Document Type: Article
UDC: 532.527, 532.5.013
MSC: 37N05, 76M23
Received: 14.08.2014
Revised: 08.09.2014

Citation: Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The dynamics of three vortex sources”, Nelin. Dinam., 10:3 (2014), 319–327

Citation in format AMSBIB
\Bibitem{BizBorMam14}
\by Ivan~A.~Bizyaev, Alexey~V.~Borisov, Ivan~S.~Mamaev
\paper The dynamics of three vortex sources
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 3
\pages 319--327
\mathnet{http://mi.mathnet.ru/nd446}


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