[ODE] Constraints: Velocity vs. Accelerations

[B P]

Hello,

I'm new to constraints, lagrange multipliers, etc so
appologies if this is too simple.

I've been reading through the various ODE docs and I
think I understand how to formulate the Jacobian for a
constraint. In the ODE manual it says somewhere:

J * v = c

J -> Jacobian
v -> velocity vector

What is c? 
How do you calculate lambda?
What is the vector you multiply the lamba's to get the
actual forces?

To sum all this questions up, given a jacobian and the
velocity vector, how do you calculate the constraint
forces? (ingoring any correction terms, CFM, etc, as
well as any upper/lower limits).

Baraff formulates constaints using accelerations,
which are more intuitively related to forces. If we
formulate a constaint with velocities, shouldn't we be
applying impulses?

Given the option, I'd like to formulate constraints
using velocities as they'd make my life a bit
easier...but I need to understand them first! :)

Thanks!






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