Relative equilibria of symmetric n-body problems on a sphere: Inverse and direct results
✍ Scribed by Chjan C. Lim
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 190 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0010-3640
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✦ Synopsis
In this paper, the author proves that the existence of a class of relative equilibria for SO(3)symmetric n-body problems on a sphere implies that these problems are in fact O(3)-symmetric in a time-reversing sense. Besides this "inverse" result, the author also proves a set of "direct" results, in which the existence of certain symmetric relative equilibria are deduced purely from symmetry considerations of the n-body problems on a sphere. The author then formulates an explicit method for the reduction of this class of symmetric Hamiltonians, which leads to symplectic shape or relative variables for the further study of the relative equilibria and equilibria. This class of problems includes the point vortex problem on a sphere, and the author applies the main results in this paper to that problem.