What is Brachistochrone curve?
[[File:Brachistochrone.gif|thumb|right|The ball on the red Brachistochrone curve reaches the other side before the other two balls.]] 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. 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]].<ref>[[I. Michael Ross|Ross, I. M.]] The Brachistochrone Paridgm, in ''A Primer on Pontryagin's Principle in Optimal Control'', Collegiate Publishers, 2009. {{ISBN|978-0-9843571-0-9}}.</ref> == References == {{Reflist}} == Other websites == {{Commons category|Brachistochrone}} * [https://arxiv.org/pdf/1401.2660.pdf The straight line, the catenary, the brachistochrone, the circle, and Fermat] Unified approach to some geodesics (from 2014) {{math-stub}} [[Category:Mathematics]] [[Category:Mechanics]]