## 30 Reputation

7 years, 288 days

## @vv It's not that I want to avoid c...

@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.

## Can solve energies with first derivative...

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

``````with(VariationalCalculus):
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:

``dsolve({L[1],f(0)=0,f(1)=1});``

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:

``````with(VariationalCalculus):
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 c...

@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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