Dynamics and statics of vortices on a plane and a sphere - I
Chaotic Dynamics
2007-05-23 v1 Exactly Solvable and Integrable Systems
Abstract
In the present paper a description of a problem of point vortices on a plane and a sphere in the "internal" variables is discussed. The hamiltonian equations of motion of vortices on a plane are built on the Lie-Poisson algebras, and in the case of vortices on a sphere on the quadratic Jacobi algebras. The last ones are obtained by deformation of the corresponding linear algebras. Some partial solutions of the systems of three and four vortices are considered. Stationary and static vortex configurations are found.
Keywords
Cite
@article{arxiv.nlin/0503049,
title = {Dynamics and statics of vortices on a plane and a sphere - I},
author = {A. V. Borisov and A. E. Pavlov},
journal= {arXiv preprint arXiv:nlin/0503049},
year = {2007}
}
Comments
16 pages, 4 figures