The Standard Momentum Map
The term momentum map (also found in the literature as moment map, a different translation of the French term application moment) is mainly used to design a mathematical construction introduced in Lie (1890), Kostant (1965), and Souriau (1965, 1966) that encodes the conservation laws associated to the symmetries of a Hamiltonian dynamical system. The choice in terminology is justified by the fact that when one deals with the translational and rotational symmetries of a simple mechanical system, the momentum map recovers the standard linear and angular momentum, respectively. The reader interested in the history of this construction is referred to Weinstein (1983b) and the remarks in § 11.2 of Marsden and Ratiu (1999).
KeywordsPoisson Bracket Symplectic Form Symplectic Manifold Poisson Structure Poisson Manifold
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