Computation and Properties of Momentum Maps

  • Jerrold E. Marsden
  • Tudor S. Ratiu
Part of the Texts in Applied Mathematics book series (TAM, volume 17)


The previous chapter gave the general theory of momentum maps. In this chapter we develop techniques for computing them. One of the most important cases is that in which we have a group action on a cotangent bundle that is obtained from lifting an action on the base via the operation of cotangent lift. These transformations are called extended point transformations. As we shall see, in this case there is an explicit formula for the momentum map, and it is always equivariant. Many of the momentum maps one meets in practical examples are of this sort.


Cotangent Bundle Infinitesimal Generator Poisson Manifold Casimir Function Hamiltonian Vector Field 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Jerrold E. Marsden
    • 1
  • Tudor S. Ratiu
    • 2
  1. 1.California Institute of TechnologyControl and Dynamical Systems, 107-81PasadenaUSA
  2. 2.Département de mathématiquesEcole polytechnique fédérale de LausanneLausanneSwitzerland

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