Hamiltonian Systems on Linear Symplectic Spaces

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


A natural arena for Hamiltonian mechanics is a symplectic or Poisson manifold. The next few chapters concentrate on the symplectic case, while Chapter 10 introduces the Poisson case. The symplectic context focuses on the symplectic two-form \( \sum {d{q^i} \wedge d{p_i}} \) and its infinite-dimensional analogues, while the Poisson context looks at the Poisson bracket as the fundamental object.


Vector Field Hamiltonian System Phase Portrait Poisson Bracket Symplectic Form 
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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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