Hi, since no one has replied (though Im greatful for the number of views), I thought I'd clarify the situation.
A ball is in contact with a plane. At the contact point, the relative velocity along the contact normal is zero. The ball's centre of mass (COM) has accn of -g. The ball is spinning at such a rate that at the contact point, the centripetal accn cancels out the gravitational accn. So the calculated contact force to prevent penetration of the point is zero.
Obviously, this will not prevent the ball penetrating the plane.
I've now looked at the equations by Baraff, Eberly and Coutinho and all get this result of zero contact force.
What am I doing wrong? Do I ignore centripetal accn (even though the above authors don't)? Is it simply an unavoidable situation that I'll to code for?
Could anyone do an example calculation for me?
Im working through "Dynamic Simulations Of Multibody Systems" by Murilo Coutinho.
Ive got a ball rigid body (B1) and a plane. I've been trying to setup the LCP problem to calculate the force require to prevent pentration.
The problem is
a = AF + b
a >= 0
F >= 0
aF = 0
a = relative acceletaion at the contact point (to solve)
A = a constant (roughly the inverse mass at the contact point)
F = relative force at the contact point (to solve)
b = current relative acceleration at contact point + relative velocity x contactFrame time derivate.
The ball has a gravity force of -10 units, and mass = 1 so -10 acceleration too.
When there is no rotation, all works fine. But when there is rotation, the contact point on the ball gets a centrepetal acceleration so its accelertaion becomes -9.
So it calculates a force of +9 to apply at the contact. But the body still has an accn of -10, so applying this force won't prevent penetration. I could just calculate the force required to prevent penetraion but that would violate the aF = 0 constraint.
I've been googling all over the place the past 2 days and im nearly bald from tearing my hair out so Id be really really grateful for any help.
I know someone posted a similate comment (Bastian1978) but it doesnt help me maintain the constraints which I need so I can extend the system to sovling multiple simultaneous contacts.
b = B1.netForce/B1.mass + (B1.inertia^-1 * B1.Torque + B1.angualMomentum X B1.W) X r1
+ B1.W X (B1.W X r1);
+ (B1.V + B1.W X r1) * (coordFrame time derivate)
A = (I * B1.invMass) - (x1 * B1.inertia^-1 * x1);
r1 = contactPoint - B1.centre of mass
x1 = r1.skewSymmetric
I = identity matrix
The final term of 'b' is zero as the contactFrame remains stationary.