VariationalMethods`
VariationalMethods`

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, ... .

Details

Examples

Basic Examples  (2)

Variational derivative for the arc length of a plane curve:

Variational derivative for the Dirichlet integral in two variables: