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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, ...], ....
Needs["VariationalMethods`"]
The Euler equations for the arc length intds in 2 dimensions yields a straight line:
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Needs["VariationalMethods`"]
A simple pendulum has the Lagrangian :
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The solution to the pendulum equation can be expressed using the function JacobiAmplitude:
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