Published November 1999
| Published
Journal Article
Open
Stability of Relative Equilibria of Point Vortices on a Sphere and Symplectic Integrators
- Creators
- Marsden, J. E.
- Pekarsky, S.
- Shkoller, S.
Chicago
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Abstract
This paper analyzes the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and the details are provided for the (integrable) case N = 3. Stability of relative equilibria is analyzed by the energy-momentum method. Explicit criteria for stability of different configurations with generic and non-generic momenta are obtained. In each case, a group of transformations is specied, such that motion in the original (unreduced) phase space is stable modulo this group. Finally, we outline the construction of a symplectic-momentum integrator for vortex dynamics on a sphere.
Additional Information
© Società Italiana di Fisica, ricevutoNov 18,1998; approvato May6,1999. The authors would like to gratefully thank P. NEWTON, A. BLAOM, G. PATRlCK and T. RATIU for their helpful comments and advice on this and related work. Paper presented at the International Workshop on "Vortex Dynamics in Geophysical Flows",Castro Marina (LE), Italy, 22-26 June 1998. The authors of this paper have agreed to not receive the proofs for correction.Attached Files
Published - MaPeSh1999.pdf
Published - ncc8138.pdf
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MaPeSh1999.pdf
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Additional details
- Eprint ID
- 20444
- Resolver ID
- CaltechAUTHORS:20101015-153037123
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2010-11-30Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field