so I'm creating a billiard ball simulation. The current version I have calculates the new position of the ball for each step, but I would like to create a math function (f(x)) for the balls position. This is not too hard, but what is really tripping me out is getting it to work with friction.

For the ball I have the following relevant information: Speed/velocity, position/startpos and friction coefficient. I am able to calculate the distance the ball moves in a single step by raising the friction coeff to the power of x. The problem is that I can only get it to work by calculating the new position step by step. I have illustrated it in Ti-Nspire:

If this is in the end is harder and less efficient that just updating each second, please let me know. If you have a solution to how I could get it as a function or a better solution, please let me know too. Thanks for any help in advance:)

CodePudding user response：

Having the velocity diminish proportionally to its current magnitude in continuous time (vs. discrete time steps) is pretty much the definition of