Definition:Hamiltonian

Definition
Let $J\sqbrk{...y_i...}$ be a functional of the form


 * $\displaystyle J\sqbrk{...y_i...}=\int_{x_0}^{x_1}\map F {x, ...y_i..., ...y_i'...}\rd x,~i=\left({1, ..., n}\right)$

Then the Hamilonian $H$ corresponding to $J\sqbrk{...y_i...}$ is defined as


 * $\displaystyle H=-F+\sum_{i=1}^n y_i' F_{y_i'}$