Definition:Hamiltonian

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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

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

This entry was named for William Rowan Hamilton.

1963: I.M. Gelfand and S.V. Fomin: Calculus of Variations ... (previous) ... (next): $\S 3.13$: Derivation of the Basic Formula