On Mon, Aug 25, 2008 at 8:40 PM, Tim Lahey <[EMAIL PROTECTED]> wrote:
> Robert,
>
> That's not what I'm looking for (I think).
> The following equation is what I normally deal with
> using LaTeX notation,
>
> \frac{d}{d t}\left(\frac{\partial L}{\partial \dot{q_i}}\right)
> = \left(\frac{\partial L}{\partial q_i}\right)
>
> where i=1,...,n and L(q_i,\dot{q_i},t). Note that q_i
> is a function of at least t. This is the Euler-Lagrange
> equation. It's the basis for most advanced dynamics.
>
> So, I want to differentiate L with respect to \dot{q_i) and
> q_i as if they were just x and t in a normal derivative.
> This is why my code replaces the functions with symbols and
> then takes the derivative with respect to these placeholder
> symbols and then reverses it.
>
> I hope I made this clearer.
The chain rule from calculus says that if f(x) = g(h(x)) then
df/dx = (dg/dh) * (dh/dx).
Dividing both sides by dh/dx we see that
dg / dh = (df /dx) / (dh/dx).
I thus suspect that when you say "differentiate g(h(x))
with respect to h" you might mean to compute dg/dh,
as defined by the chain rule above.
William
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