Definition:Hamiltonian

Definition
Let $J[...y_i...]$ be a functional of the form


 * $\displaystyle J[...y_i...]=\int_{x_0}^{x_1}F\left({x, ...y_i..., ...y_i'...}\right)\mathrm{d}{x},~i=\left({1, ..., n}\right)$

Then the Hamilonian $H$ corresponding to $J[...y_i...]$ is defined as


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