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, …, q_n, ∂φ/∂ q₁, …, ∂φ/∂ q_n, t) + ∂φ/∂ t = 0, where q₁, …, q_nare 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.

单词	hamilton-jacobi equation
释义	Hamilton-Jacobi equation 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, …, q_n, ∂φ/∂ q₁, …, ∂φ/∂ q_n, t) + ∂φ/∂ t = 0, where q₁, …, q_nare 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. AcronymsSeeHJE
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