Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published June 4, 1996 | public
Report Open

Hamiltonian G-Spaces with regular momenta

Blaom, Anthony

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.

Additional Information

This is a revision of CIT-CDS 95-033. http://resolver.caltech.edu/CaltechCDSTR:1995.033 Formerly writing as Anthony D. Perry

Files

CDS96-008.pdf
Files (2.2 MB)
Name Size Download all
md5:1a35f547cba3fb48bf5355c869305161
2.2 MB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 24, 2023