How to Simulate a Bouncing and Spinning Ball in Two Dimensions?

[gcoope]

I'm looking to simulate a bouncing and spinning ball in two dimensions. I have the detection working fine but I'm having a little difficulty with the physics.

I have a moving ball colliding with a stationary immovable wall.

I would like to know the resultant velocities of the ball in terms of:

initial velocity u,
initial angular velocity ω,
radius r,
coefficient of friction μ
coefficient of restitution e,
mass m,
moment of intertia I

obviously first we resolve normally to the plane.

we have vj = -e*uj

so the impulse = m(1+e)uj

now I think there should be a rotational impulse proportional to this by a factor of the coefficient of friction,
so ω increases by μm(1+e)uj/I

but I get stuck here. I haven't considered the initial angular velocity of the ball and its impact on the resultant velocity and resultant angular velocity.

I hope someone can be of help,

thanks a lot,

Giles.

 

[kuruman]

I'm looking to simulate a bouncing and spinning ball in two dimensions.

You can't unless you impose constraints on how the ball is spinning, i.e. the orientation of the spin axis. Say you define the motion of the ball in the "collision plane" which is defined as the plane formed by the initial velocity vector and the normal to the surface. Now assume that the ball is spinning and that, while the ball is in contact with the surface, the point of contact on the ball does not slide relative to the point of contact on the surface. If you want the velocity of the ball after the collision to remain in the collision plane, the spin axis must be in a plane perpendicular to both the surface and the collision plane. Now note that the collision of this kind conserves angular momentum about the point of contact P because there are no torques about that point acting the ball. You need to conserve angular momentum about point P to relate the "after" quantities to the "before" quantities. After the collision the component of the angular velocity perpendicular to the collision plane becomes $V_{CM}/R$ where $V_{CM$ is the velocity of the center of mass.