Geodesic
A new integrable problem of motion of point vortices on the sphere
Russian journal of nonlinear dynamics, Tome 3 (2007) no. 2, pp. 211-223.

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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, reduction, bifurcation analysis.
Mots-clés : point vortex 
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A. V. Borisov; A. A. Kilin; I. S. Mamaev. A new integrable problem of motion of point vortices on the sphere. Russian journal of nonlinear dynamics, Tome 3 (2007) no. 2, pp. 211-223. http://geodesic.mathdoc.fr/item/ND_2007_3_2_a5/