Characterizations of Roller Coaster Surface According to Ribbon Frame

Roller coasters are usual examples of energy transformation, with an interaction of kinetic and potential energy as the train moves surrounding the curves, loops, hills and valleys of the path.. A roller coaster path so that a particle moving in space will stay on a given curve in space. The roller coaster surface is a special type of spherical surfaces. In this study, ？-Roller Coaster surfaces with Ribbon frame is investigate in Euclidean 3-space. Moreover, the Gaussian curvature, mean curvature, first and second fundamental form of coefficients of Roller Coaster surfaces of are examined. Then, the parallel surfaces of ？-Roller Coaster surfaces of are obtained. Finally, we derive the related equations for the inextensible flow of a ？ -Roller Coaster surface