Ball bouncing and rotating off of surface

[gammastate]

I am working on a simulation where a ball is dropped from a random height with some x component of velocity and y velocity being zero. When the ball hits the surface it should bounce off with a spin. Here's what I've thought up of so far:

In the first case the \omega is zero. When the ball hits the ground there will be static friction and the ball will roll with a velocity of vx, energy conservation can be used to solve for the new velocity since the angular velocity will already be known (\omega = vx/r). The new components of linear velocity can be found by taking the new magnitude divided by the old magnitude and multiplying each component of velocity respectively.

For nonzero \omega I suppose that kinetic friction would have to be used.

I'm not sure that this is a correct way of going about it (momentum is not conserved [first case] and I also have a coefficient for which the y velocity decreases so that it bounces back to a lower height)

Any thoughts/resources on this would be of greatly appreciated.

 

[rcgldr]

In the case where the ball is not initially spinning, and if the friction is not zero, the ball's linear speed will decrease and it's angular speed will increase when it hits the ground. How much change occurs depends on the compressive (linear) and shear (angular) elasticity of the ball and the ground.