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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2006, Volume 2, Number 2, Pages 181–192
(Mi nd161)
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This article is cited in 1 scientific paper (total in 1 paper)
Dynamics of two vortex rings on a sphere
A. V. Borisovab, I. S. Mamaevab a Udmurt State University
b Institute of Computer Science
Abstract:
The motion of two vortex rings on a sphere is considered. This motion generalizes the well-known centrally symmetrical solution of the equations of point vortex dynamics on a plane derived by D. N. Goryachev and H. Aref. The equations of motion in this case are shown to be Liouville integrable, and an explicit reduction to a Hamiltonian system with one degree of freedom is described. Two particular cases in which the solutions are periodical are presented. Explicit quadratures are given for these solutions. Phase portraits are described and bifurcation diagrams are shown for centrally symmetrical motion of four vortices on a sphere.
Keywords:
vortex, Hamiltonian, motion on a sphere, phase portrait.
Citation:
A. V. Borisov, I. S. Mamaev, “Dynamics of two vortex rings on a sphere”, Nelin. Dinam., 2:2 (2006), 181–192
Linking options:
https://www.mathnet.ru/eng/nd161 https://www.mathnet.ru/eng/nd/v2/i2/p181
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Abstract page: | 253 | Full-text PDF : | 93 | First page: | 1 |
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