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Hamiltonian G-Spaces with regular momenta

Blaom, Anthony (1996) Hamiltonian G-Spaces with regular momenta. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1996.008

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Abstract

Let G be a compact connected non-Abelian Lie group and let (P, w, G, J) be a Hamiltonian G-space. Call this space a G-space with regular momenta if J(P) ⊂ g*reg, where g*reg ⊂ g* denotes the regular points of the co-adjoint action of G. Here problems involving a G-space with regular momenta are reduced to problems in an associated lower dimensional Hamiltonian T-space, where T ⊂ G is a maximal torus. For example two such G-spaces are shown to be equivalent if and only if they have equivalent associated T-spaces. We also give a new construction of a normal form that has appeared in Dazord and Delzant (1987), for integrable G-spaces with regular momenta. We show that this construction, which is a kind of non-Abelian generalization of action-angle coordinates, can be reduced to constructing conventional action-angle coordinates in the associated T-space. In particular the normal form applies globally if the action-angle coordinates can be constructed globally. We illustrate our results in concrete examples from mechanics, including the rigid body. We also indicate applications to Hamiltonian perturbation theory.


Item Type:Report or Paper (Technical Report)
Additional Information:This is a revision of CIT-CDS 95-033. http://resolver.caltech.edu/CaltechCDSTR:1995.033 Formerly writing as Anthony D. Perry
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:1996.008
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1996.008
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28118
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:07 Dec 2007
Last Modified:26 Dec 2012 14:30

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