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The Hamilton-Jacobi equation is a first-order nonlinear partial differential equation that arises in variational calculus and which gives, in particular, a formulation of the laws of motion in classical mechanics.
It relates the principal function (action functional as a function of certain arguments) with the Hamiltonian. In one dimension it is of the form
Specifically for quadratic Hamiltonians:
Last revised on January 2, 2015 at 17:16:59. See the history of this page for a list of all contributions to it.