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Topic: Brachistochrone
Replies: 1   Last Post: Mar 13, 2013 8:26 AM

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Posts: 1,562
Registered: 11/8/10
Re: Brachistochrone
Posted: Mar 13, 2013 8:26 AM
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"Melissa" wrote in message <khp06m$seh$1@newscl01ah.mathworks.com>...
> Hey! I'm trying to model a brachistochrone curve given a start and end point(randomly chosen). I'm not sure how to implement the parametric equations of the model with just two points to start off. Any suggestions?

Let A=(x1,y1) and B=(x2,y2) be the two randomly chosen points
(where the points are ordered such that y2>y1).
Then the parametric Brachistochrone curve between the two points is given by
The other condition the curve has to fulfill is that it passes through A.
for a certain value t*.
This is a system of two equations in two unknowns (R and t*).
Once you have determined R and t*, the curve (x(t),y(t)) for t in [0:t*]
is the brachistochrone curve you want to determine.
You may solve the two-equation-system using MATLAB's fsolve or you may
eliminate R and solve the equation
for t* using MATLAB's fzero.

Best wishes

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