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
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 $\textbf {y}$
Brachistochrone problem for 3 points - Physics Stack Exchange Yes, but one first has to generalize the classical 2-point Brachistochrone problem A B where the initial speed vA traditionally is zero, to the case where the initial speed vA may be non-zero but fixed The solution to this initial speed Brachistochrone problem (assuming no friction) is still a cycloid Now consider the 3-points Brachistochrone problem A B C with initial speed vA The speed vB
Brachistochrone problem with drag - Physics Stack Exchange The original Brachistochrone problem is without friction and drag The Brachistochrone problem can also be solved analytically with friction But what would the optimal path be if there was a drag