Geodesic
On the dynamics of two point vortices in an annular region
Russian journal of nonlinear dynamics, Tome 6 (2010) no. 3, pp. 531-548

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In this paper, the system of two vortices in an annular region is shown to be integrable in the sense of Liouville. A few methods for analysis of the dynamics of integrable systems are discussed and these methods are then applied to the study of possible motions of two vortices of equal in magnitude intensities. Using the previously established fact of the existence of relative choreographies, the absolute motions of the vortices are classified in respect to the corresponding regions in the phase portrait of the reduced system.
Mots-clés : point vortex, equations of motion, vortex pair.
Keywords: reduction, bifurcational diagram, relative choreographies 
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     author = {V. V. Vaskin and N. N. Erdakova},
     title = {On the dynamics of two point vortices in an annular region},
     journal = {Russian journal of nonlinear dynamics},
     pages = {531--548},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2010_6_3_a4/}
}
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V. V. Vaskin; N. N. Erdakova. On the dynamics of two point vortices in an annular region. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 3, pp. 531-548. http://geodesic.mathdoc.fr/item/ND_2010_6_3_a4/