Optimal Halfpipe - dynamic programing - Education

thingiverse

An ideal halfpipe is one that has the fastest path between 2 horizontal points driven solely by gravity. Here's a "half" of an optimal halfpipe - if you have the quickest route to the middle, the other half must look exactly the same! I added a straight comparison curve and it's significantly slower! It's a "calculus of variations"-problem, see Leonhard Euler and Joseph-Louis Lagrange. But I calculate it using "Finite Elements" and a "Dynamic Programming" approach, see Richard Ernest Bellman. I disregard rotation and rolling resistance as well as aerodynamic drag of the ball. The size of the model doesn't matter; it's always the same curve! I also created a small startbox to start both iron balls simultaneously.