Are you familiar with cycloid curve?
@YL explained to us that curve of fastest descent is about finding a shape of curve connecting two points with different height, while minimizing descending time. The solution to the problem is "cycloid curve."
With many solutions to this problem already, he thought it would be interesting if there is one using modern technology, FE-simulation and optimization (SIMULIA Abaqus and Isight). In the video below, the blue curve shows analytical solution (cycloid), and red curve is the one to be optimized. The red curve is divided into 6-segments and 5 y-coordinate values are adjusted to minimize descending time using "Nelder-Mead" algorithm. Interestingly, you can see the red curve converges to cycloid.
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