Timeline for Brachistochrone problem for 3 points

6 events

when toggle format	what		by	license	comment
Aug 2, 2019 at 9:06	comment	added	Qmechanic♦		Notes for later: $1+ (\frac{dx}{dy})^2=\frac{k^2}{y}$. Rescale $x$ and $y$ so that $k^2=2$. Then $\frac{dx}{dy}= +(\frac{2}{y}-1)^{-1/2}=\sqrt{\frac{y}{2-y}}$ with antiderivative $x=\arctan \frac{\sqrt{y(2-y)}}{1-y}-\sqrt{y(2-y)}=\theta-\sin\theta$, where $1-y=\cos\theta$.
May 6, 2012 at 19:14	vote	accept	Mathlover
May 6, 2012 at 19:13	vote	accept	Mathlover
May 6, 2012 at 19:13
May 6, 2012 at 6:46	comment	added	Qmechanic♦		Here I'm considering the idealized Brachistochrone problem where solution curves are allowed to be only piecewise smooth. Instantaneous change of velocity is provided by an idealized (infinitely big) normal force, which does no work.
May 5, 2012 at 22:13	comment	added	tmac		what about y'? You would still need continuity there, this is not guaranteed with two patched together solutions.
May 5, 2012 at 21:37	history	answered	Qmechanic♦	CC BY-SA 3.0