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Nelin. Dinam., 2007, Volume 3, Number 2, Pages 211–223 (Mi nd135)  

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

A new integrable problem of motion of point vortices on the sphere

A. V. Borisovab, A. A. Kilinab, I. S. Mamaevab

a Udmurt State University
b Institute of Computer Science

Abstract: The dynamics of an antipodal vortex on a sphere (a point vortex plus its antipode with opposite circulation) is considered. It is shown that the system of $n$ antipodal vortices can be reduced by four dimensions (two degrees of freedom). The cases $n=2,3$ are explored in greater detail both analytically and numerically. We discuss Thomson, collinear and isosceles configurations of antipodal vortices and study their bifurcations.

Keywords: hydrodynamics, ideal fluid, vortex dynamics, point vortex, reduction, bifurcation analysis.

Full text: PDF file (298 kB)

Document Type: Article
UDC: 532.517
MSC: 37N10, 76M23, 35Q35
Received: 17.06.2007

Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “A new integrable problem of motion of point vortices on the sphere”, Nelin. Dinam., 3:2 (2007), 211–223

Citation in format AMSBIB
\Bibitem{BorKilMam07}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper A new integrable problem of motion of point vortices on the sphere
\jour Nelin. Dinam.
\yr 2007
\vol 3
\issue 2
\pages 211--223
\mathnet{http://mi.mathnet.ru/nd135}


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  • http://mi.mathnet.ru/eng/nd135
  • http://mi.mathnet.ru/eng/nd/v3/i2/p211

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    This publication is cited in the following articles:
    1. Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “The Spatial Problem of 2 Bodies on a Sphere. Reduction and Stochasticity”, Regul. Chaotic Dyn., 21:5 (2016), 556–580  mathnet  crossref  mathscinet  zmath  elib
  • Нелинейная динамика
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