I'm learning how to make a small physic engine. I read some different articles dealing with rigid body dynamics and simulation, and I recently found Erin Catto's document titled "Iterative Dynamics with Temporal Coherence". I have already done a little physic engine mainly based on a document from David Baraff : it uses timeswap technique to prevent from interpenetration and it builds a linear system to constraint relative velocities between bodies. Although this is in theory correct, it is hard to implement and I have a lot of problems (with bouncing and also timeswap: sometimes I have infinite responses because the step found was 0 seconds !). So I decided to rewrote a big part of the engine since I prefer Erin Catto's approach.
I understood the equations established in his document. However, I'm stuck at page 14, where the final equation is written:
J * B * lambda = µ
where J is the Jacobian for the contacts, lamba the vector of forces magnitudes, µ a big term (including InvMass, Bias, initial Velocity) and B = inv(M) * J^T
J^T is the orthogonal matrix of J.
I understood that I must solve J B lambda = µ and find the vector lambda, but I don't have the J^T matrix ? Is there anyway to compute this matrix from J ? Maybe there is something I didn't understand correctly.
Thank you in advance for all your responses !
(sorry for my English, I'm french )
- this is simple. I did some confusion but now I understand (I hope !). Thanks a lot for your help (and also your really helpfull document).