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_n 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.