Angular Momenta of Relative Equilibrium Motions and Real Moment Map Geometry
Dynamical Systems
2016-09-21 v1 Representation Theory
Symplectic Geometry
Abstract
Chenciner and Jimenez Perez showed that the range of the spectra of the angular momenta of all the rigid motions of a fixed central configuration in a general Euclidean space form a convex polytope. In this note we explain how this result follows from a general real convexity theorem of O Shea and Sjamaar in symplectic geometry. Finally, we provide a representation theoretic description of the pushforward of the normalized measure under the real moment map for Riemannian symmetric pairs.
Keywords
Cite
@article{arxiv.1505.07331,
title = {Angular Momenta of Relative Equilibrium Motions and Real Moment Map Geometry},
author = {Gert Heckman and Lei Zhao},
journal= {arXiv preprint arXiv:1505.07331},
year = {2016}
}
Comments
23 pages