I'm working through the Brachistochrone Problem but I get stuck at the differential equation:
(eq. 13)
The solution is supposed to be in the form of two parametric functions and , so I tried switching to polar coordinates and manipulating the equation in various ways. But that lead me to some hairy integrals, and I want to find out if I'm on the right track before I continue.
What's the best approach here?
Look at the article that you posted earlier. Take a look at equations 30 - 33. Specifically take a look at the substitution in equation 31. That's the key to integrating the problem, but I'm afraid that I can't make it work. If you like you can work backward and verify that satisfy the differential equation. (It's fussy about the details, but isn't too hard overall.) That's as far as I can go with it.
-Dan