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, whereq₁, …,q_nare generalized coordinates,tis the time coordinate,His 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.