Marsden, Jerrold E. and Weinstein, Alan J. (1974) Reduction of symplectic manifolds with symmetry. Reports on Mathematical Physics, 5 (1). pp. 121-130. ISSN 0034-4877. doi:10.1016/0034-4877(74)90021-4. https://resolver.caltech.edu/CaltechAUTHORS:20100910-101924768
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Abstract
We give a unified framework for the construction of symplectic manifolds from systems with symmetries. Several physical and mathematical examples are given; for instance, we obtain Kostant’s result on the symplectic structure of the orbits under the coadjoint representation of a Lie group. The framework also allows us to give a simple derivation of Smale's criterion for relative equilibria. We apply our scheme to various systems, including rotationally invariant systems, the rigid body, fluid flow, and general relativity.
Item Type: | Article | |||||||||
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Additional Information: | © 1974 Published by Elsevier Science Ltd. Received September 15, 1972. Available online 22 March 2002. Partially supported by NSF Grant GP-15735. Partially supported by NSF Grant GP-34785x and a Sloan Fellowship. | |||||||||
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Issue or Number: | 1 | |||||||||
DOI: | 10.1016/0034-4877(74)90021-4 | |||||||||
Record Number: | CaltechAUTHORS:20100910-101924768 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100910-101924768 | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 19864 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | Ruth Sustaita | |||||||||
Deposited On: | 10 Sep 2010 18:00 | |||||||||
Last Modified: | 08 Nov 2021 23:55 |
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