# Hamiltonian Systems on Linear Symplectic Spaces

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

## Abstract

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.

## Keywords

Vector Field Hamiltonian System Phase Portrait Poisson Bracket Symplectic Form
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