[ODE] Constraint equations and the famous J matrix

[Joakim Eriksson]

I have been trying to figure out how exactly a constraint system
works for a while and I just wanted to run this buy you guys.
Someone here should be able to tell me if I'm on the right track
and if not what I have missed.
If nothing else this might help others in my situation because
I have never seen all this information collected in one place.

So lets start with the equations:

A*lambda=b
      -1 T
A = JM  J
       -1
b =-(JM  F+c)

So in the abover equations we have:
lambda = The unknowns we want to find
J      = The jacobian constraint matrix
M      = The mass matrix
F      = External forces that exists in the system

Now for a small example. Say I want to constrain a body
to a world position. What would I have to do to get that to work?
                          -1
First we need to fill in M  so it should look something like:
A-----
-B----
--C---
---DEF
---GHI
---JKL

In the abover ascii drawing A-C is linear inverse mass and D-L is
rotational inverse mass.

If we ignore joint positional (error) fixing c is 0

But in this abover case what does the J matrix look like?
>From joint.pdf (Good doc BTW) I guess that the J matrix would look
like this

1-----
-1----
--1---
----QN
---O-P
---QM-

Where M-O is the positive (x,y,z) anchor point and P-R is the anchor
point neged. In otherwords the lower left is a matrix representation
of a vector cross product with the anchor point.

Is this a correct J matrix for this example or am I way off here?

Cheers
 Joakim E.