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SOLUTIONS
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| Variational Methods Package Symbol | Tutorials »|See Also »|More About » |
| 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, ...], .... |
Needs["VariationalMethods`"] The Euler equations for the arc length  in 2 dimensions yields a straight line:
Needs["VariationalMethods`"] A simple pendulum has the Lagrangian  :
The solution to the pendulum equation can be expressed using the function JacobiAmplitude: |
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