alecjacobson

30 Reputation

4 Badges

5 years, 357 days

MaplePrimes Activity


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:

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 command line interface to Maple and viewing the online help in my usual web browser (Safari or Chrome). 

Page 1 of 1