Jump effect of an eccentric cylinder rolling on an inclined plane

Abstract

Abstract This work addresses the intriguing phenomenon of the jump effect exhibited by an eccentric cylinder rolling on an inclined plane. Our main objective is to determine the region of the parameter space where the cylinder can undergo a jump after pure rolling motion. In previous works, it was assumed that slipping always precedes a jump, leading to the belief that slip is necessary. In contrast, our study challenges this prevailing notion by demonstrating the existence of situations where a jump can occur after pure rolling motion. We present a detailed theoretical description of the jump effect, investigating the dependence of the jump behavior on the initial conditions, the forces involved, and the parameter values. Through rigorous analysis, we determine the restricted region in the parameter space that allows for jumps to occur without slipping. Our findings contribute to the ongoing debate surrounding the jump effect in eccentric cylinder dynamics.