The Brachistochrone Problem and Solution Calculus of Variations

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=zYOAUG8PxyM

In this video, I set up and solve the brachistochrone problem, which involves determining the path of shortest travel in the presence of a downward gravitational field. This is done using the techniques of Calculus of Variations, and it will turn out that the brachistochrone can be represented by the parametric equations of a cycloid. • The Brachistochrone is a rather popular topic on Youtube, with pop-science channels like VSauce making videos about it. However, not many people actually derive the equations, so I'm hopeful that this tutorial will be a more rigorous change of pace. • Questions/requests? Let me know in the comments! • Prereqs: The first three videos of this playlist: • Calculus of Variations • Euler-Lagrange Video: • Derivation of the Euler-Lagrange Equa... • Lecture Notes: https://drive.google.com/file/d/0BzC4... • Patreon: https://www.patreon.com/user?u=4354534 • Twitter: https://twitter.com/FacultyOfKhan?lan... • Patreon Supporters: • Jennifer Helfman • Jacob Soares • Yenyo Pal

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