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Variational Methods Package
VARIATIONAL METHODS PACKAGE SYMBOL

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,…],….

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Basic Examples  (2)Basic Examples  (2)

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The Euler equations for the arc length in two dimensions yields a straight line:

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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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Scope  (4)Scope  (4)

Applications  (3)Applications  (3)

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