I just find how have the English Page of the Mathcurves.com !
One more time the Symdrom of Edgard Allan Poe of he Purloined Letter has made a victim ! :)
And what about my silly conjecture of the Orient / Line - Line use ?
@Bemfarmer here are the rules guiding the curve(shown in red but not accurate).
Basically point A needs to be tangent to ground plane and the height of point B needs to be 5 feet or so but cannot go beyond vertical(ideally 70-80 degrees).
The existing CycloidInterp script will work, with aRadius = bRadius = 2.5 feet+, mirrored upside down, using half of one cycle.
At a radius of 2.5 feet, the height difference is 5 feet, and the upper tangent is 90 degrees.
At a radius of 3 feet, the height difference is 6 feet, and with one vertical foot removed from the top of the cycloid,
the tangent is about 65.9052 degrees from the horizontal, as measured with Michael's Angle script.
Some more options may be added to the script...
- Brian
(No calculus needed. It has already been proven that without friction, the brachistochrone is a cycloid)
(The CycloidInterp script uses the Trochoid formula. When aRadius = bRadius, the trochoid is a common cycloid)
Brachistochrones.JPG
