Very cool! But I do not think this post shows the actual Brachistochrone curve, right? Also, for the oscillatory curve, should / could not the ball jump a bit? Or the problem somehow is formulated not for a ball, but for a bid on a wire?
Well, I only assume the ball have one degree of freedom
Yes, you are right, using the parametric expression is only a compromise when the explicit analytic expression cannot be obtained.
