Let be a G-principal fiber bundle. The action of G on the cotangent bundle is free and Hamiltonian. By Liberman and Marle [Symplectic Geometry and Analytical Mechanics (Reidel, Dortrecht, 1987)] and Marsden and Ratiu [Lett. Math. Phys. 11, 161 (1981)] the quotient space is a Poisson manifold. We will determine the Poisson bracket on the reduced Poisson manifold and its symplectic leaves.
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Research Article| July 01 1999
Phase space reduction and Poisson structure
Nadhem Zaalani; Phase space reduction and Poisson structure. J. Math. Phys. 1 July 1999; 40 (7): 3431–3438. https://doi.org/10.1063/1.532897
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