Problem with the Theory of Erin Catto's paper

[Dani3L]

I'm studying the paper "Iterative Dynamics with Temporal Coherence" from Erin Catto.

I'm trying to apply the theory of this paper to a very simple situation where two spheres collide. One sphere is moving at velocity v and collide with another sphere that is not moving. According to me, if the two spheres have the same mass, after the collision, the sphere that was moving will stop and the other sphere will begin to move with velocity v. I tried to compute this scenario with the theory in the paper of Erin Catto but I don't find the same result (I found that after the collision both spheres move in the same direction with velocity v/2).

Here is a short document where I have detailled my computations that I obtained with the theory of Catto's paper. The computations are very simple because the problem contains only one contact constraint.

I would appreciate if someone can have a look at my problem because I don't understand where I'm wrong !

[bone]

I think you're missing some sort of restitution coefficient (I don't remember if that is addressed in Catto's paper). With zero restitution, a.k.a. a plastic collision, the contact constraint will simply solve the impulse needed to prevent further penetration ... in other words the resulting velocity difference at the contact point becomes exactly zero, so *of course* they will now be going the same speed.

With restitution, they bounce off of each other. If they are perfectly elastic (as opposed to the plastic collision above), which we typically represent as a restitution of 1.0, then I think your solution is the result - the first ball stops and the second ball goes at the original velocity of the first.

I might suggest searching this board or look in the Bullet source code to see exactly where to apply the coefficient of restitution.

[Dirk Gregorius]

Instead of the bias (position error correction) use the relative velocity along the contact normal on the right hand side.

[Dani3L]

Thank you for your answers both of you. It was really helpful.

The modification proposed by Dirk Gregorius seems to be what I was looking for and seems to work.

[hop]

Could you please explain which equation's right hand side you substituted for the relative velocity?