Uploaded October 2017 | Updated September 2026, 2 weeks ago
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: youtube.com/playlist?list=PLdgVBOaXkb9CD8igcUr9Fmn5WXLpE8ZE_
Euler-Lagrange Video: youtube.com/watch?v=sFqp2lCEvwM
Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4TmE4T0dGNzZLMEU/view?usp=sharing&resourcekey=0-fqZd3apIVOEaepISFtixVQ
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan?lang=en
Patreon Supporters:
Jennifer Helfman
Jacob Soares
Yenyo Pal
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: youtube.com/playlist?list=PLdgVBOaXkb9CD8igcUr9Fmn5WXLpE8ZE_
Euler-Lagrange Video: youtube.com/watch?v=sFqp2lCEvwM
Lecture Notes: drive.google.com/file/d/0BzC45hep01Q4TmE4T0dGNzZLMEU/view?usp=sharing&resourcekey=0-fqZd3apIVOEaepISFtixVQ
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan?lang=en
Patreon Supporters:
Jennifer Helfman
Jacob Soares
Yenyo Pal
