You can make a lot of simplifications to make this problem solvable. For example, friction is a very complicated phenomenon. Simplify it to be a proportional to the velocity of the ball and consistent between materials. You can model the motion of the ball using standard physics equations for velocity and acceleration with friction taken into account in addition to the vertical slope of channel it is traveling in.

You can use a library like the Wykobi Computational Geometry Library[^] to calculate where the center of the ball will be while riding in the channel. Given the dimensions of a v-shaped channel and the radius of the ball, you can calculate the center point of the ball throughout its motion.

This all depends on how you model the physical structures the model will traverse. I like to combine mathematics and computer graphics (see my avatar and profile) and I would consider how the objects will be rendered in setting up the models. The modelling structure should accommodate both physics calculations and rendering.

I would structure the modelling to work in terms of time slices, as if you were rendering this as an animation. Movies are, generally, rendered at 24 FPS but you may want to target 30 or 60 Hertz meaning you will have a time slice of 33.3 or 16.7 mS. You could say, nah, we'll go with 20mS for 50Hz rendering so the numbers work out evenly. What ever. The point is, the whole simulation will start with the ball at an initial position in your physical structure. That is frame 1 of your animation. The next step in time will be 20mS later so calculate where the ball will be after 20mS of motion from an initial velocity of zero and the initial position. After 20mS the ball will have new poosition, velocity, and acceleration vectors and those will provide the initial conditions for the next time step's calculations. Continue this for as long as you want the simulation to run.

The calculations for motion down a straight v-shaped channel are fairly straight forward for the physics-inclined. It gets a bit trickier when the channel curves. There have to be some centrifugal deceleration effects accounted for in the curve so there are some challenges involved.

I hope that gives you some hints on how to approach this. A good 3D vector library will be essential. There are lots of them around. For my stuff I wrote my own but I don't recommend this approach. I wanted the learning experience and I found it to be quite valuable. Anyway, the first thing I would do is decide what development environment and language you want to use for this. There are lots and lots of good possibilities to choose from. Best of luck with it.

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