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The Optimal Momentum Map

In: Geometry, Mechanics, and Dynamics

Author

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  • Juan-Pablo Ortega
  • Tudor S. Ratiu

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.

Suggested Citation

  • Juan-Pablo Ortega & Tudor S. Ratiu, 2002. "The Optimal Momentum Map," Springer Books, in: Paul Newton & Philip Holmes & Alan Weinstein (ed.), Geometry, Mechanics, and Dynamics, chapter 11, pages 329-362, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-21791-8_11
    DOI: 10.1007/0-387-21791-6_11
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