The state of each ball can be described by 9 parameters: the current location of the center of mass (x,y,z), the current linear velocity (vx, vy, xz) and the angular velocity on 3 axes.
I don't think the forces acting on the rails need to be similar -- they just need to be such that the acceleration of the ball is always parallel to the track. Unfortunately the equation of motion will look pretty ugly and optimizing the system will be quite a challenge.
And finally, the system has to be stable, ie. small perturbations should be cancelled rather than grow - if a ball gets a little too fast there should be something like a bend that slows it down, but that bend should at the same time not slow down a ball that is already too slow...
Another parameter - as a track designer you can manipulate the width of the track to change the ball speed. It raises and lowers the ball on the track, changing both the rolling diameter and the center of gravity. This can be used to make subtle changes to the ball speed before a turn.
The state of each ball can be described by 9 parameters: the current location of the center of mass (x,y,z), the current linear velocity (vx, vy, xz) and the angular velocity on 3 axes.
I don't think the forces acting on the rails need to be similar -- they just need to be such that the acceleration of the ball is always parallel to the track. Unfortunately the equation of motion will look pretty ugly and optimizing the system will be quite a challenge.
And finally, the system has to be stable, ie. small perturbations should be cancelled rather than grow - if a ball gets a little too fast there should be something like a bend that slows it down, but that bend should at the same time not slow down a ball that is already too slow...