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. http://resolver.caltech.edu/CaltechAUTHORS:20100910-101924768
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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.
|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.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||10 Sep 2010 18:00|
|Last Modified:||22 Jul 2013 23:06|
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