Spheroid rolling up on diverging inclines

Abstract

Objects rolling upward on diverging inclined rails exhibit a counterintuitive behavior that has intrigued physicists and students alike. Among the most well-known is the double-cone paradox, where a cone appears to roll uphill due to the geometry of the rails. In this paper, we extend this idea to more general rigid bodies, including spheres and ellipsoids. We examine the physical conditions under which this motion occurs, and we derive the necessary geometric and energetic constraints using analytical mechanics. We then validate our theoretical models through carefully designed experiments.