The brachistochrone problem asks what shape a hill should be so a ball slides down in the least time. The tautochrone problem asks what shape yields an oscillation frequency that is independent of …

Jun 11, 2010 · The discussion centers on the brachistochrone problem, which identifies the cycloid as the optimal ramp shape for minimizing travel time for a ball rolling down. Participants confirm that the …

Feb 19, 2025 · The Brachistochrone problem is usually presented with the having a ball dropped into the slide with initially zero velocity and at position $(x, y)=(0, 0)$. I would like to know the more general so...

Aug 1, 2013 · The solution to the brachistochrone problem is a cycloid curve rather than a straight line due to the need to optimize both path length and average speed under gravitational influence. A …

Jan 3, 2023 · The brachistochrone curve is one that not only goes down but also comes up. This seems like a problem for me, because when you look at the equation above, the right-hand side always gets …

Jul 3, 2023 · It seems to be the same answer, just expressed very differently and very much more difficult to get the answer from the method avoiding Beltrami identity. Why should textbook authors …

Nov 3, 2020 · Hello, There is a physics problem called the Brachistochrone problem which I know has been solved for 0 initial velocity (assumes 0 friction and only...

Oct 13, 2025 · The discussion focuses on minimizing the functional for the Brachistochrone problem, specifically using the Euler-Lagrange equation. The functional to minimize is presented as an integral …

Jun 29, 2024 · When I came across the Brachistochrone problem, my teacher said we could relate it to Fermat's principle of least time. So, we could make many glass slabs of high $\\mathrm dx$, and …

Apr 28, 2024 · How to prove that the Brachistochrone problem could be reduced to finding a curve on a plane? Ask Question Asked 1 year, 7 months ago Modified 1 year, 7 months ago