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- Is there an intuitive reason the brachistochrone and the tautochrone . . .
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
- Brachistochrone Problem w Initial Velocity - Physics Forums
The discussion centers on the Brachistochrone problem, specifically addressing the scenario where an object has an initial velocity The original problem has been solved for zero initial velocity, yielding a cycloid as the optimal path The poster is seeking a formula for determining the quickest route between two horizontal points with a specified initial velocity, having calculated a travel
- Why Does a Cycloid Curve Minimize Travel Time? - Physics Forums
The discussion centers on the brachistochrone problem, which identifies the cycloid curve as the optimal path for minimizing travel time for a ball rolling down a ramp Participants note that the cycloid allows for a steeper initial incline, providing the ball with a higher initial velocity, which contributes to a faster descent compared to a straight ramp The conversation highlights the
- Why do I need the Beltrami identity to solve the brachistochrone problem?
Why do I need the Beltrami identity to solve the brachistochrone problem? Ask Question Asked 2 years, 4 months ago Modified 8 months ago
- lagrangian formalism - Solution of Brachistochrone Problem with . . .
Solution of Brachistochrone Problem with friction Ask Question Asked 2 years, 3 months ago Modified 2 years, 3 months ago
- energy conservation - Brachistochrone problem with initial velocity . . .
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
- variational principle - Another Solution To Brachistochrone Problem . . .
Another Solution To Brachistochrone Problem Ask Question Asked 4 years, 11 months ago Modified 1 year, 4 months ago
- Evaluating the integral in the brachistochrone problem numerically
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 same value for any given value of $\textbf {y}$
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