Motion of vortex sources on a plane and a sphere

Details Motion of vortex sources on a plane and a sphere Motion of vortex sources on a plane and a sphere

2005-07-27

arxiv.org/abs/nlin/0507060v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, 4 figures

Scientific paper

The Equations of motion of vortex sources (examined earlier by Fridman and Polubarinova) are studied, and the problems of their being Hamiltonian and integrable are discussed. A system of two vortex sources and three sources-sinks was examined. Their behavior was found to be regular. Qualitative analysis of this system was made, and the class of Liouville integrable systems is considered. Particular solutions analogous to the homothetic configurations in celestial mechanics are given.

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