Randomised Bead Machine/Pachinko Problem.

Hello, I am writing code for Bead Machine problem and while there is no problem with standard model I have some issues with model in which nails are distributed randomly. While horizontal randomization can be resolved by having random chance of ball falling to the right or to the left using random number generator, vertical randomization doesn't look as obvious for me. Do you have any ideas how to implement vertical randomization?

Answer 1

[Walter Roberson]

The ball does not simply fall to one side or the other of the peg: the ball bounces off the peg, with the peg vibrating and acting as a bit of a spring. The curved upward bounce might intersect the bottom or side of a peg above the first, leading to a spring-pushed bounce away or down. With the vertical positions not always the same, the velocities obtained are not always going to be the same....

So you model in the acceleration and spring effects and do path planning and a bunch of testing for for intersection...

[Adil Baitenov]

Thank you for the answer, but in my model pegs are not vibrating and balls don't bounce, because it is the model for particle scattering.

[Walter Roberson]

However, you are writing code for the Bead Machine problem, and in the Bead Machine, the pegs do vibrate and beads do bounce and are acted upon by gravity but not by electromagnetic fields or strong or nuclear forces.

If you change your mind and decide to model a different system, then we would need to know the properties of the other system to best advise.

[Adil Baitenov]

I am sorry for misleading in my question. Basically the model is the stream of particles going through the media filled with scattering cylinders distributed randomly. The results of periodic structure correspond to results of mathematical model of bead machine, so I decided to modify it in order to proceed.

[Walter Roberson]

Are the scattering cylinders perfect reflectors? Such that upon scattering, each particle keeps 100% of its momentum but is scattered according to standard angle-of-reflection criteria? And there is no fluid or gravity to consider? What size are the cylinders compared to the particles? Are either one considered points for this purpose?

[Adil Baitenov]

Yes, cylinders are perfect reflectors and there is no fluid or gravity. Cylinders are about 4 times bigger than particles.