VariationalMethods`
VariationalMethods`EulerEquations
EulerEquations[f,u[x],x]
returns the Euler–Lagrange differential equation obeyed by u[x] derived from the functional f, where f depends on the function u[x] and its derivatives, as well as the independent variable x.
EulerEquations[f,u[x,y,…],{x,y,…}]
returns the Euler–Lagrange differential equation obeyed by u[x,y,…].
EulerEquations[f,{u[x,y,…],v[x,y,…],…},{x,y,…}]
returns a list of Euler–Lagrange differential equations obeyed by u[x,y,…],v[x,y,…],….
Details
- To use EulerEquations, you first need to load the Variational Methods Package using Needs["VariationalMethods`"].
Examples
open allclose allBasic Examples (2)
| In[1]:= |
The Euler equations for the arc length 
in two dimensions yields a straight line:
| In[1]:= |
A simple pendulum has the Lagrangian 
:
The solution to the pendulum equation can be expressed using the function JacobiAmplitude:
