Optimal Halfpipe - dynamic programing - Education
thingiverse
An optimal halfpipe is one that has the fastest line between 2 horizontal points only driven by gravity. Here is a "half" of an optimal halfpipe - if you have the fastest way to the middle, the other half have to look the same! I added a straight comparison curve and it is much slower! It it a "calculus of variations"-problem, see Leonhard Euler und Joseph-Louis Lagrange. But I calculate it with "Finite Elements" and a "Dynamic Programming" Idea, see Richard Ernest Bellman. I neglect rotation and rolling resistance as well as aerodynamic drag of the ball. The size of model doesn't matter, it is always the same curve! I made also a little startbox to start the two iron ball simultaneous.
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