**Geometry of Hamiltonian Systems**

A Hamiltonian system may be understood as a fiber bundle *E* over time *R*, with the fibers *E*_{t}, *t* ∈ *R*, being the position space. The Lagrangian is thus a function on the jet bundle *J* over *E*; taking the fiberwise Legendre transform of the Lagrangian produces a function on the dual bundle over time whose fiber at *t* is the cotangent space *T***E*_{t}, which comes equipped with a natural symplectic form, and this latter function is the Hamiltonian.

Read more about this topic: Hamiltonian Mechanics

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