Lie Groups. Momentum Mappings. Reduction.
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In this chapter we describe the symplectic reduction procedure due to Marsden and Weinstein  which generalizes the classical theorems of Liouville and Jacobi on the elimination of the node and the fixing of the center of mass in the n-body problem, as well as the coadjoint orbit’s theorem. This method is also significant in various physical examples.
KeywordsCotangent Bundle Momentum Mapping Coadjoint Orbit Reduce Phase Space Spherical Pendulum
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