Аннотация:
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.
Ключевые слова:
point vortices, integrable dynamics, perturbation theory.
Поступила в редакцию: 20.11.2007 Принята в печать: 26.12.2007
Образец цитирования:
A. I. Gudimenko, “Dynamics of Perturbed Equilateral and Collinear Сonfigurations of Three Point Vortices”, Regul. Chaotic Dyn., 13:2 (2008), 85–95
\RBibitem{Gud08}
\by A.~I.~Gudimenko
\paper Dynamics of Perturbed Equilateral and Collinear Сonfigurations of Three Point Vortices
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 2
\pages 85--95
\mathnet{http://mi.mathnet.ru/rcd563}
\crossref{https://doi.org/10.1134/S1560354708020032}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2395528}
\zmath{https://zbmath.org/?q=an:1229.37116}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd563
https://www.mathnet.ru/rus/rcd/v13/i2/p85
Эта публикация цитируется в следующих 8 статьяx:
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 37
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 1
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 179
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 317
M. A. Sokolovskiy, K. V. Koshel, J. Verron, “Three-vortex quasi-geostrophic dynamics in a two-layer fluid. Part 1. Analysis of relative and absolute motions”, J. Fluid Mech., 717 (2013), 232
A. I. Gudimenko, A. D. Zakharenko, “Stability of the relative equilibrium of three vortex charges with zero total intensity”, Fluid Dyn, 47:4 (2012), 465
А. И. Гудименко, А. Д. Захаренко, “Качественный анализ относительного движения трех вихрей”, Нелинейная динам., 6:2 (2010), 307–326
А. И. Гудименко, А. Д. Захаренко, “Движение трех вихрей с нулевой суммарной интенсивностью”, Прикл. мех. техн. физ., 51:3 (2010), 55–65; A. I. Gudimenko, A. D. Zakharenko, “Three-vortex motion with zero total circulation”, J. Appl. Mech. Tech. Phys., 51:3 (2010), 343–352
Цитирование в формате AMSBIB
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