On Sun, Dec 14, 2008 at 03:18:10PM +0800, Aaron Yu ZHANG wrote:
> Hi Friedrich,
>
> I think I made the question even more misleading by giving the previous
> example. In fact, please look into [1]this equation.
Ok. But I didnt change my opinion about the previous solution :-) I hope
I can explain it way.
> Basically, T is a function of qi and qi_dot, which can be derived.
What you say is that:
T: R^2 --> R
(qi, qi_dot) |--> T(qi, qi_dot)
T maps the two real numbers (qi and qi_dot) to an other real number.
> qi is a function of time,
So this is:
qi = f(t)
Remember to school: y = f(x) x,y are real numbers and f is the function.
Now you concatanate the functions T and f and get a new function which
depends from t:
t |--> T( f(t), f'(t))
> I've no problem get diff(T,qi). But I cannot derive diff(T,qi_dot)
That isnt a problem because you want derivate T with respect to the first
and second argument (qi and qi_dot):
T_qi (qi, qi_dot)
and
T_qi_dot (qi, qi_dot)
The derivatives of T, namly T_qi and T_qi_dot, are also functions of
qi and qi_dot. And then you concatanate T_qi and T_qi_dot with f:
t |--> T_qi( f(t), f'(t))
and
t |--> T_qi_dot( f(t), f'(t))
These are functions which depends from t. The last function should
be derivate with respect to t to get Qj.
The point is: T and f are different function and must be concatenate
(substitute). If this was not clear you must ask again :-)
By,
Friedrich
> Now, I have this idea:
>
> % isympy
> In [1]: var('t xDot')
> Out[1]: (t, xDot)
>
> In [2]: g = lambdify((x, xDot), x*xDot)
>
> In [3]: g(x, xDot)
> Out[3]: x*xDot
>
> In [4]: g(f(t), diff(f(t), t))
> Out[4]:
> d
> f(t)*──(f(t))
> dt
>
> In [5]: gDot = lambdify((x, xDot), diff(g(x, xDot), xDot))
>
> In [6]: gDot(f(t), diff(f(t), t))
> Out[6]: f(t)
> By,
>
> Friedrich
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