Sign in to follow this  
Mr_Nick

Resolving contact force to prevent penetration and LCP

Recommended Posts

Hello,
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

where
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.

Formule are:

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);

where:
r1 = contactPoint - B1.centre of mass
x1 = r1.skewSymmetric
I = identity matrix

The final term of 'b' is zero as the contactFrame remains stationary.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this