Variational Methods Package Symbol

VariationalD

VariationalD[f, u[x], x]
returns the variational derivative of the integral

with respect to u[x], where the integrand f is a function of u, its derivatives, and x.

VariationalD[f, u[x, y, ...], {x, y, ...}]
returns the variational derivative of the multiple integral

with respect to u[x, y, ...], where f is a function of u, its derivatives and the coordinates x, y, ....

VariationalD[f, {u[x, y, ...], v[x, y, ...], ...}, {x, y, ...}]
gives a list of variational derivatives with respect to u, v, ....

To use VariationalD, you first need to load the Variational Methods Package using Needs["VariationalMethods`"].

Variational derivative for the arc length

of a plane curve:

Variational derivative for the Dirichlet integral in two variables:

Needs["VariationalMethods`"]

Variational derivative for the arc length

of a plane curve:

Needs["VariationalMethods`"]

Variational derivative for the Dirichlet integral in two variables: