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Lie algebras in vortex dynamics and celestial mechanics - IV | | A.V. Bolsinov
; A.V. Borisov
; I.S. Mamaev
; | | Date: |
30 Mar 2005 | | Journal: | Regular and Chaotic Dynamics, 1999 Volume 4 Number 1 | | Subject: | Chaotic Dynamics; Exactly Solvable and Integrable Systems | nlin.CD nlin.SI | | Abstract: | The work of A.V. Borisov, A.E. Pavlov, Dynamics and Statics of Vortices on a Plane and a Sphere - I (Reg. & Ch. Dynamics, 1998, Vol. 3, No 1, p.28-39) introduces a naive description of dynamics of point vortices on a plane in terms of variables of distances and areas which generate Lie-Poisson structure. Using this approach a qualitative description of dynamics of point vortices on a plane and a sphere is obtained in the works Dynamics of Three Vortices on a Plane and a Sphere - II. General compact case by A.V. Borisov, V.G. Lebedev (Reg. & Ch. Dynamics, 1998, Vol. 3, No 2, p.99-114), Dynamics of three vortices on a plane and a sphere - III. Noncompact case. Problem of collaps and scattering by A.V. Borisov, V.G. Lebedev (Reg. & Ch. Dynamics, 1998, Vol. 3, No 4, p.76-90). In this paper we consider more formal constructions of the general problem of n vortices on a plane and a sphere. The developed methods of algebraization are also applied to the classical problem of the reduction in the three-body problem. | | Source: | arXiv, nlin.CD/0503066 | | Services: | Forum | Review | PDF | Favorites | |
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