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Chenciner and Jimenez Perez showed that the range of the spectra of theangular momenta of all the rigid motions of a fixed central configuration in ageneral Euclidean space form a convex polytope. In this note we explain howthis result follows from a general real convexity theorem of O Shea and Sjamaarin symplectic geometry. Finally, we provide a representation theoreticdescription of the pushforward of the normalized measure under the real momentmap for Riemannian symmetric pairs.

Angular Momenta of Relative Equilibrium Motions and Real Moment Map Geometry