Understanding constraint equations

[cboyce]

I've been doing a lot of reading to try to understand more concepts in game physics, and one thing I've been having a hard time on is conceptualizing constraint equations. If I were constrain a particle in 3D space on to the surface of a sphere, for example, the position constraint x^2+y^2+z^z - R^2 = 0 is intuitive the me. Beyond that though, I'm not sure how other constraints and forces come into play. Assuming the particle has a velocity of 0 at the first time step, and the only external force is gravity, how do I continue on to calculate the constraint force? I realize this might not be a straight forward question, and part of what I'm trying to do is determine what underlying concepts I need to understand better to approach this problem.

[Dirk Gregorius]

I think that such very generic questions are very hard to answer on a forum. Did you look at the material Erwin posted here: http://bulletphysics.org/Bullet/phpBB3/ ... p?f=6&t=63

[bone]

To narrow it down a bit, I would probably start with the paper "Iterative Dynamics with Temporal Coherence" by Erin Catto. It's short enough to read and understand in a day, and fairly easy to implement, too. After that, I'd probably look at Kenny Erleben's thesis for more details.

[cboyce]

Thanks for the information, I've been doing a lot of reading over the past few days. I'm still working on connecting the dots. Say I have my position constraint equation for a single particle, C=x^2+y^2+z^2=0. In Erin Catto's paper, he says to determine the Jacobian, we need to differentiate C with respect to time. My calculus is a bit rusty, but I thought that differentiating C with respect to time would give us C' = 2x dx/dt + 2y dy/dt + 2z dz/dt. Is this going in the right direction?