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.

 

[PJC01]

for sharing your simulation of collisions between pool balls. It sounds like you have a good understanding of the basic principles involved, such as the conservation of momentum and the transfer of kinetic energy between objects during a collision. The addition of rotational momentum and friction will certainly add more complexity to your simulation, but it will also make it more accurate and realistic.

Regarding your question about collisions between a single ball and a cluster of balls, there are a few factors to consider. Firstly, the mass of the cluster will have an effect on the overall outcome of the collision. As you mentioned, a larger mass will result in a greater bounce back effect. This is because the larger mass will resist the impact of the white ball and cause it to rebound with more force.

Another factor to consider is the distribution of mass within the cluster. If the mass is evenly distributed, then the white ball may bounce off in a predictable direction. However, if the mass is more concentrated in certain areas, the white ball may bounce off in a different direction due to the uneven distribution of force.

In terms of determining the mass of each individual ball within the cluster, you could use a formula based on the size and density of the balls. This would give you a rough estimate, but keep in mind that the actual mass of each ball may vary slightly due to imperfections in the material or air pockets inside the ball.

Lastly, it's important to keep in mind that your simulation will never be an exact representation of real life. There are many variables at play in a real collision, such as the surface friction, the angle of impact, and the elasticity of the balls. It's always a good idea to compare your simulation results to real-life observations and make adjustments as needed. Good luck with your simulation!