There is already support in the git master for taking derivatives with
respect to functions and derivatives:
In [153]: diff(x*f(x)**2 + f(x)*diff(f(x), x), f(x))
Out[153]:
d
2⋅x⋅f(x) + ──(f(x))
dx
In [154]: diff(x*f(x)**2 + f(x)*diff(f(x), x), diff(f(x), x))
Out[154]: f(x)
So your boilerplate code would be unnecessary in SymPy.
>From what I remember, Gilbert used this to implement some degree of
Euler-Lagrange in the mechanics module. You'll have to ask him or
look at the code for the specifics, though.
Aaron Meurer
On Fri, Mar 23, 2012 at 4:39 PM, Tim Lahey <tim.la...@gmail.com> wrote:
> On Fri, Mar 23, 2012 at 5:33 PM, Elliot Marshall <marshall2...@gmail.com>
> wrote:
>> For example, I would like to write the functions necessary so that, using
>> sympy.physics.mechanics, one could use Euler, Lagrange, and possibly other
>> methods to find the dynamical equations of motion for a system.
>
> I assume you mean Euler-Lagrange? I'd like to see it progress to
> handling variables that vary spatially and not just in time. That
> said, I'd like Euler-Lagrange support as well. Supporting vector
> variables (in a linear algebra sense) would be nice as well. I believe
> there's been work on symbolic matrix expressions in Sympy. This would
> allow for the derivation of finite element equations.
>
> Implementing just Euler-Lagrange shouldn't take too long if one is
> familiar with the programming of the module. I expect probably a few
> weeks to a month at most. My implementation of E-L in Maple is less
> than a page of code, most of that is converting from a function to a
> variable that can be differentiated and back. There will be a bit
> setting things up for the E-L equation, but some can probably be
> reused from the current module.
>
> Cheers,
>
> Tim.
>
> --
> Tim Lahey
> PhD Candidate, Systems Design Engineering
> University of Waterloo
> http://about.me/tjlahey
>
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