Abstract
The presence of symmetries in a Hamiltonian system usually simplies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or Marsden-Weinstein reduction procedure takes advantage of this and associates to the original system a new Hamiltonian system with fewer degrees of freedom. However, in a large number of situations, this standard approach does not work or is not e cient enough, in the sense that it does not use all the information encoded in the symmetry of the system. In this work, a new momentum map will be defined that is capable of overcoming most of the problems encountered in the traditional approach.
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To Jerry Marsden on the occasion of his 60th birthday
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Ortega, JP., Ratiu, T.S. (2002). The Optimal Momentum Map. In: Newton, P., Holmes, P., Weinstein, A. (eds) Geometry, Mechanics, and Dynamics. Springer, New York, NY. https://doi.org/10.1007/0-387-21791-6_11
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DOI: https://doi.org/10.1007/0-387-21791-6_11
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