Definition:Hamilton-Jacobi Equation
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Definition
Let $\map S {x_0, x_1, \mathbf y} = \map S {x, \mathbf y}$ be the geodetic distance, where $x_0$ is fixed and $x_1 = x$.
Let $H$ be Hamiltonian.
- $\ds \frac {\partial S} {\partial x} + \map H {x, \mathbf y, \nabla_{\mathbf y} S} = 0$
is known as the Hamilton-Jacobi Equation.
Source of Name
This entry was named for William Rowan Hamilton and Carl Gustav Jacob Jacobi.
Also see
Sources
- 1963: I.M. Gelfand and S.V. Fomin: Calculus of Variations ... (previous) ... (next): $\S 4.23$: The Hamilton-Jacobi Equation. Jacobi's Theorem