Momentum Maps

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


In this chapter we show how to obtain conserved quantities for Lagrangian and Hamiltonian systems with symmetries. This is done using the concept of a momentum mapping, which is a geometric generalization of the classical linear and angular momentum. This concept is more than a mathematical reformulation of a concept that simply describes the well-known Noether theorem. Rather, it is a rich concept that is ubiquitous in the modern developments of geometric mechanics. It has led to surprising insights into many areas of mechanics and geometry.


Angular Momentum Symplectic Manifold Infinitesimal Generator Coadjoint Orbit Poisson Manifold 
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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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