This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 VARIATIONAL METHODS PACKAGE SYMBOL

# EulerEquations

 returns the Euler-Lagrange differential equation obeyed by derived from the functional f, where f depends on the function and its derivatives as well as the independent variable x. returns the Euler-Lagrange differential equation obeyed by . returns a list of Euler-Lagrange differential equations obeyed by .
The Euler equations for the arc length in 2 dimensions yields a straight line:
A simple pendulum has the Lagrangian :
The solution to the pendulum equation can be expressed using the function JacobiAmplitude:
Needs["VariationalMethods`"]
The Euler equations for the arc length in 2 dimensions yields a straight line:
 Out[2]=
 Out[3]=

Needs["VariationalMethods`"]
A simple pendulum has the Lagrangian :
 Out[2]=
The solution to the pendulum equation can be expressed using the function JacobiAmplitude:
 Out[3]=
 Scope   (4)
The Lagrangian of a point particle in 2 dimensions has 2 dependent variables, and yields Newton's equations:
The Lagrangian of a point particle in 2 dimensions with a central potential:
Second- and higher-order derivatives may be included in the integrand. A Lagrangian for motion on a spring using higher-order terms:
The integrand has several independent variables:
The Euler equations yield Laplace's equation:
 Applications   (3)
The Euler equations for the integrand :