Geodesic
Dynamics of perturbed equilateral and collinear configurations of three point vortices
Russian journal of nonlinear dynamics, Tome 3 (2007) no. 4, pp. 379-391.

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Dynamics of perturbed stable equilateral and collinear configurations of three point vortices in an incompressible ideal fluid is studied. The asymptotics of the perturbed motion to the unperturbed one is obtained. It is shown that in the first approximation in a appropriate coordinate system the vortices rotate about their undisturbed positions in elliptical orbits. The velocity of the rotation is calculated. It is shown that the eccentricities of the orbits are coincide. The ratio of major axes of any two orbits is calculated. In case of equilateral configuration this ratio is equal to the ratio of inverse intensities of the corresponding vortices. The angle between major axes of any two orbits of the vortices is calculated. In case of equilateral configuration this angle is $\pm 120$ degrees.
Keywords: point vortices, integrable dynamics, perturbation theory. 
@article{ND_2007_3_4_a0,
     author = {A. I. Gudimenko},
     title = {Dynamics of perturbed equilateral and collinear configurations of three point vortices},
     journal = {Russian journal of nonlinear dynamics},
     pages = {379--391},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2007_3_4_a0/}
}
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A. I. Gudimenko. Dynamics of perturbed equilateral and collinear configurations of three point vortices. Russian journal of nonlinear dynamics, Tome 3 (2007) no. 4, pp. 379-391. http://geodesic.mathdoc.fr/item/ND_2007_3_4_a0/