Brachistochrone Curve Representation via Transition Curve
Rabiatul Adawiah Fadzar, Md Yushalify Misro · Mathematics and Statistics · 2023
The brachistochrone curve is an optimal curve that allows the fastest descent path of an object to slide frictionlessly under the influence of a uniform gravitational field. In this paper, the Brachistochrone curve will be reconstructed using two different basis functions, namely Bézier curve and trigonometric Bézier curve with shape parameters. The Brachistochrone curve between two points will be approximated via a C-shape transition curve. The travel time and curvature will be evaluated and compared for each curve. This research revealed that the trigonometric Bézier curve provides the closest approximation of Brachistochrone curve in terms of travel time estimation, and shape parameters in trigonometric Bézier curve provide better shape adjustability than Bézier curve.