Angular momenta of relative equilibrium motions and real moment map geometry. (English) Zbl 1379.70041
Summary: A. Chenciner and H. Jiménez-Pérez [Mosc. Math. J. 13, No. 4, 621–630 (2013; Zbl 1366.70015)] 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 convexity theorem of L. O’Shea and R. Sjamaar in real moment map geometry [Math. Ann. 317, No. 3, 415–457 (2000; Zbl 0985.37056)]. Finally, we provide a representation-theoretic description of the pushforward of the normalized measure under the real moment map for Riemannian symmetric pairs.
MSC:
| 70F10 | \(n\)-body problems |
| 17B20 | Simple, semisimple, reductive (super)algebras |
| 22E30 | Analysis on real and complex Lie groups |
| 53D20 | Momentum maps; symplectic reduction |
| 70G10 | Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics |
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