nLab
Hamilton-Jacobi equation

Context

Physics

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Contents

Idea

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

St+H(t,x,Sx)=0 \frac{\partial S}{\partial t} + H\left(t, x, \frac{\partial S}{\partial x}\right) = 0

References

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.