Handling Spin in Billiard Collisions



A quick question.

I'm trying to write a snooker-simulator. Know it is the physics that bothers me. The situation is:
Two balls collide with each other. The have known velocities and also known spin-velocities around the z-axle. Know I wonder:

Is it correct to treat the spinning and the translations separately in the collision (Saying so means that I treat the angular momentum (Iw), the spinning energy (Iw^2)/2), the linear momentym (mv) and the kinetic energy as constants before and after the collision).


Here are a few immediate thoughts on your problem. I would welcome more dialog if these ideas trigger any reaction from you.

It is correct to treat the angular momentum, linear momentum and kinetic energy due to translation as conserved quantities under the usual assumptions of billiard ball collisions, that is all collisions are elastic and there is negligible friction energy loss during the time of observation.

It seems to me that these assumptions render the spin irrelevant. If there is no friction between the ball surfaces, then the spinning ball will slide along the non-spinning ball without affecting it. If any of the spin is to be coupled from ball to ball. then the conservation of rotational energy will be compromised.

Perhaps to determine how much spin is coupled from the projectile ball to the target ball you could assume something of the details of the interaction of the two balls. One approach might be to assume that the surfaces are perfectly rough (no slipping) relative to each other and perfectly smooth (complete slipping) relative to the table. This conserves translational kinetic energy but you still have to deal with the friction loss in rotational kinetic energy. Also I wonder about the fact that the balls after the collision will spin in opposite directions. This will give the angular momentum vectors the opposite sense, one up and one down. Somehow these have to add up to the angular momentum vector of the incoming ball.

Now, even if you surmount the above difficulties and correctly model the transfer of rotational momentum and energy from one ball to the other, unless you allow for some friction between the balls and the table the fact that the balls are spinning about the z axis can have no effect of curving their post collision trajectory, contrary to reality.

To more accurately model a real world collision between a spinning and a non-spinning ball, you need to account for the friction between the balls and the table and the resultant spin about the x and y axes, together with any tumbling, that is changing the orientation in space of the x, y and z axes. I have not tried to write such a complete model, but I suspect you are in for a rough time of it.