Brachistochrone curve
curve connecting two points such that a bead sliding frictionlessly in a uniform gravitational field moves to the other endpoint the fastest
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.[1]
References
change- ↑ 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.
Other websites
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Wikimedia Commons has media related to Brachistochrone.
- The straight line, the catenary, the brachistochrone, the circle, and Fermat Unified approach to some geodesics (from 2014)
