EulerEquations

EulerEquations[f,u[x],x]

returns the EulerLagrange 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 EulerLagrange differential equation obeyed by u[x,y,].

EulerEquations[f,{u[x,y,],v[x,y,],},{x,y,}]

returns a list of EulerLagrange differential equations obeyed by u[x,y,],v[x,y,],.

Details

Examples

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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)

Applications  (3)

See Also

VariationalD

Tutorials