CaltechAUTHORS
  A Caltech Library Service

Reduction of symplectic manifolds with symmetry

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

[img] PDF - Published Version
Restricted to Repository administrators only
See Usage Policy.

1307Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20100910-101924768

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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/0034-4877(74)90021-4DOIUNSPECIFIED
http://www.cds.caltech.edu/~marsden/bib/1974/01-MaWe1974/MaWe1974.pdfAuthorUNSPECIFIED
ORCID:
AuthorORCID
Weinstein, Alan J. 0000-0002-0928-6784
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.
Funders:
Funding AgencyGrant Number
NSFGP-15735
NSFGP-34785x
Sloan FellowshipUNSPECIFIED
Record Number:CaltechAUTHORS:20100910-101924768
Persistent URL:http://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:22 Jul 2013 23:06

Repository Staff Only: item control page