Collision of a sphere into a cluster of spheres (billiard balls)

[brigadier90]

Hello all,

I am attempting to simulate collisions of pool balls. For the moment i am doing so without taking rotational momentum or friction between balls into account. right now i have a system that successfully simulates a collision between 1 ball and another ball. Here's how it basically works:

(assuming object ball is stationary)

The object ball basically gets or absorbs the white ball's velocity component along the x-axis (the axis axis being the line passing through the centers of both balls) while the white ball retains the y component of its original velocity. therefore in my simulation a straight shot (or a full ball shot) would make the while ball stop and the obj ball absorbs all its velocity. Ofc my simulation also works for arbitrary velocities for any number of balls.

The problem i am having is i can't figure out what happens when the while ball collides into a cluster of balls(e.g break shot). I know that in real life the white ball basically bounces back. i am guessing this is due to the cluster having a larger mass collectively. In my algorithm, increasing the mass of one of the balls does generate that 'bounce back' effect. However when dealing with a cluster, how do i know by how much to increase the mass for each collision, both between the white ball and the cluster, and the other internal collisions that happen whithin the cluster. Can anyone help?

Thank you

 

[mfb]

You can split the collision into many collisions between the individual balls. Add some randomness in the precise ball positions, and this could give a realistic simulation.

 

[brigadier90]

yeah but that wouldn't cause the bounce back effect would it? for the bounce back effect i was thinking when the white ball hits a ball that is stuck to many other balls (e.g on the break) i could increase the mass of that ball that was struck depending on how many other balls are stuck or frozen to it. then the 2 balls that that ball hits (furthur down the balls triangle) would also have an increase in mass depending on the balls behind them. But increasing the mass depends on the angle of velocity, of the white ball and the angle of the object balls velocity after that, I have no idea and cannot find any articles that discuss this issue and i really need the equations.

 

[mfb]

I would expect that you can get backwards motion with 2-ball-collisions only.