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These are replies submitted by alecjacobson

@vv It's not that I want to avoid calculus of variations, I want Maple to apply calculus of variations for me rather than me having to do it by hand. I'd like a generic solution for energy functionals involving any number of derivatives.

So, I figured out a way to solve the example above:

E := diff(f(t),t)^2:
L :=EulerLagrange(E,t,f(t)):

so far this will output:

        L :={-2*diff(diff(x(t),t),t),-diff(x(t),t)^2= K[2],2*diff(x(t),t)= K[1]}

Finally solve with the boundary conditions using:


which will output

         t(t)= t

but I'm not sure how to go about solving this for energy functionals involving second derivatives. For example:

E := diff(f(t),t,t)^2:
L :=EulerLagrange(E,t,f(t)):

this gives an error 

Error, (in D/procedure) Unable to differentiate procedures containing diff: Use D

In this case I know that the euler lagrange equation should be (up to scale) f''''(t) = 0 and that the solution is f(t) = 3*t^2-2*t^3

How do I get there?

@rlopez thanks, but I'm using the command line interface to Maple and viewing the online help in my usual web browser (Safari or Chrome). 

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