[ODE] ODE's Jacobian matrices

[Gary R. Van Sickle]

> A question for the math & ODE-internals inclined:
>
> I am confused about the calculation of ODE's
> constraint jacobians.  I've read "How to make new
> joints in ODE".  The suggested procedure for
> calculating jacobians there is to first create a
> position constraint equation C(q) = 0, then take the
> time derivative of that, then rearrange until you have
> a matrix times linear velocity and a matrix times
> angular velocity for the bodies involved.  These
> matrices are then your jacobians.  This doesn't agree
> with any of my studies with regards to jacobian
> matrices...
>
> When I have a set of functions C1 through Cm of
> variables q1 through qn, I calculate the jacobian by
> taking the partial derivative of each C1 through Cm
> with respect to q1 through qn, and I'm left with an m
> row, n column matrix which is my jacobian.
>
> What is the connection between these two methods?  How
> does the ODE procedure avoid the need to take partial
> derivatives?
>

"first create a position constraint equation C(q) = 0, then take the time
derivative of that" - isn't the "time derivative" spoken of actually the partial
derivatives wrt time of C(q)?

--
Gary R. Van Sickle
Brewer.  Patriot.