43, Baltiyskaya Street, Vladivostok, 690041, Russia
V.I.Il`ichev Pacific Oceanological Institute of the Far Eastern Branch of Russian Academy of Sciences
Gudimenko A. I.
Dynamics of Perturbed Equilateral and Collinear Сonfigurations of Three Point Vortices
2008, vol. 13, no. 2, pp. 85-95
Using the technique of asymptotic expansions, we calculate trajectories of three point vortices in the vicinity of stable equilateral or collinear configurations. We show that in an appropriate rotating coordinate system each vortex moves in an elliptic orbit. The orbits of the vortices have equal eccentricities. The angle and ratio between the major axes of any two orbits have a simple analytic representation.