[ODE] ODE Source code vs. Baraff

[Sergio Valverde]

>> A*lamda = b (plus some stuff for the LCP solver to simulate friction and
>> limits..)
>> where:
>> invM = inverse of Mass matrix, Fext = external forces (and torques)
>> A = J * invM * J'  (I got this one!)
>>b = -(J * invM * Fext + c) (here's my problem)

I think that it is not necessary to find the equivalence between ODE
and Baraff's formulation. I spent some efforts on that with little
success (of course, due to my limited mathematical abilities ;-)

>> Am I misinterpretting lamda, or is its definition
>> slightly different in your implementation?  If so, how can I reformulate
>>  the problem so that:

>> for i = 0 to iterations
>>   for each joint in island (world for now)
>>    (S1) calculate rhs = f(body->facc, body->tacc)...
>>    (S2) dSolveLCP(A, lamda, rhs, lo, hi, other stuff)
>>    (S3) add J * lamda to accumulators
>>  next joint
>> next i
(S4) Integration

In fact, the simple solution we have outlined in past e-mails is 
quite similar to your scheme. In fact, the same ODE source code gives 
clues to formulating the "iterative" algorithm.  Using  dSolveLCP
simplifies a lot and also (because already performs some sort of
 error reduction) limits the number of iterations until convergence.

Step S1 (PrepareLCP): The code for computing A and RHS for a single 
joint can be  adapted from the existing ODE source code for computing 
A and RHS with (multiple) joints.  Note that the single joint A matrix
 is equivalent to computing the diagonal blocks of the multiple 
joints A matrix.

Steps S2 (SolveLCP) and S3 (Acumulate): Don't need any adjustment at all. 
Simply pass the right parameters for the single joint scenario.

Step S4 (Integration): Don't forget to integrate using MoveAndRotate

Also, I found useful to precompute the inertia matrices first (probably
along with the A matrices)

Sergi