This question is not specifically about Bullet, but it's related to the derivation of the contact constraint used in Box2D. I apologise if this is not the correct forum for this question, but it didn't seem to attract any attention on the Box2D forum, so I thought someone here might be able to answer.
From Erin Catto's paper "Iterative Dynamics With Temporal Coherence" he states that when we calculate Cdot for the contact (normal) constraint, we use the product rule and get two terms, one which is essentially the velocity dotted with the normal, and the other which is the penetration dotted with the derivative of the normal. His paper goes on to say that the second term can be neglected when we make the assumption that the penetration is small. What I'm wondering is, why is this a valid assumption? Particularly when (as in the paper) discrete collision detection is being used, doesn't that mean that the penetration can be arbitrarily deep, depending on the velocities and sizes of the interacting bodies?
The other question I have is, since Cdot is always going to be linear in the velocity (and will be equal to JV) doesn't that mean that we should still be able to rearrange the equation for Cdot into JV, with both of these terms (ie without neglecting the second term)? Would it not be more accurate to do so?
Thanks
![Smile :)](./images/smilies/icon_smile.gif)