Hamilton-Jacobi equation


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Hamilton-Jacobi equation

[′ham·əl·tən jə′kō·bē i‚kwā·zhən]
(mathematics)
A particular partial differential equation useful in studying certain systems of ordinary equations arising in the calculus of variations, dynamics, and optics: H (q1, …, qn , ∂φ/∂ q1, …, ∂φ/∂ qn , t) + ∂φ/∂ t = 0, where q1, …, qn are generalized coordinates, t is the time coordinate, H is the Hamiltonian function, and φ is a function that generates a transformation by means of which the generalized coordinates and momenta may be expressed in terms of new generalized coordinates and momenta which are constants of motion.
References in periodicals archive ?
which is the Hamilton-Jacobi equation (27) for m=0.
A similar solution of the Hamilton-Jacobi equation can be obtained for massive particles.
In adition, we get the Hamilton-Jacobi equation [E.
However, the Hamilton-Jacobi equation gives access to the action function, which may provide a relationship between some integrals of motion.
The Hamilton-Jacobi equation admits another kind of motion too, the quantum motion.
With the substitution E [right arrow] i[eta][delta]/[delta]t and p [right arrow] i[eta] [delta]/[delta]r in the Hamilton-Jacobi equation in the flat space we get the Klein-Gordon equation
Other topics include homogenization of stochastic Hamilton-Jacobi equations, general relative entropy in a nonlinear McKendrick model, pointwise Fourier inversion in analysis and geometry, and a class of one-dimensional Markov processes with continuous paths.

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