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

Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]

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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2014, Volume 10, Number 3, Pages 319–327 (Mi nd446)

The dynamics of three vortex sources

Ivan A. Bizyaev^a, Alexey V. Borisov^ab, Ivan S. Mamaev^ba

^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

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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 system’s configurations is obtained. Possible phase portraits and various relative equilibria of the system are presented.

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

Received: 14.08.2014
Revised: 08.09.2014

Document Type: Article

UDC: 532.527, 532.5.013

MSC: 37N05, 76M23

Language: Russian

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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https://www.mathnet.ru/eng/nd446

https://www.mathnet.ru/eng/nd/v10/i3/p319

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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