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Relative equilibria of point vortices on the sphere
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UNSPECIFIED (2001) Relative equilibria of point vortices on the sphere. PHYSICA D-NONLINEAR PHENOMENA, 148 (1-2). pp. 97-135. ISSN 0167-2789.
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Abstract
We prove the existence of many different symmetry types of relative equilibria for systems of identical point vortices on a non-rotating sphere. The proofs use the rotational symmetry group SO(3) and the resulting conservation laws, the time-reversing reflectional symmetries in O(3), and the finite symmetry group of permutations of identical vortices. Results include both global existence theorems and local results on bifurcations from equilibria. A more detailed study is made of relative equilibria which consist of two parallel rings with n vortices in each rotating about a common axis. The paper ends with discussions of the bifurcation diagrams for systems of 3-6 identical vortices. (C) 2001 Elsevier Science B.V. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | PHYSICA D-NONLINEAR PHENOMENA | ||||
Publisher: | ELSEVIER SCIENCE BV | ||||
ISSN: | 0167-2789 | ||||
Official Date: | 1 January 2001 | ||||
Dates: |
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Volume: | 148 | ||||
Number: | 1-2 | ||||
Number of Pages: | 39 | ||||
Page Range: | pp. 97-135 | ||||
Publication Status: | Published |
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