Contents

# 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

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