Brachistochrone curve

A Brachistochrone curve is the fastest path for a ball to roll between two points that are at different heights. A ball can roll along the curve faster than a straight line between the points. And the bottom one would be faster then the top.

The curve will always be the quickest route regardless of how strong gravity is or how heavy the object is. However, it might not be the quickest if there is friction.

The curve can be found using calculus of variations and optimal control.Ross, I. M. The Brachistochrone Paridgm, in A Primer on Pontryagin's Principle in Optimal Control, Collegiate Publishers, 2009. .
 References 

 Other websites 

 The straight line, the catenary, the brachistochrone, the circle, and Fermat Unified approach to some geodesics (from 2014)

Category:Mathematics
Category:Mechanics