Dynamics and statics of vortices on a plane and a sphere - I

Details Dynamics and statics of vortices on a plane and a sphere - I Dynamics and statics of vortices on a plane and a sphere - I

2005-03-23

arxiv.org/abs/nlin/0503049v1

Regular and Chaotic Dynamics, 1998 Volume 3 Number 1

Nonlinear Sciences

Chaotic Dynamics

16 pages, 4 figures

Scientific paper

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.

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