The jump effect of a general eccentric cylinder rolling on a ramp

Abstract

Interesting phenomena occur when an eccentric rigid body rolls on an inclined or horizontal plane. For example, a variety of motions between rolling and sliding are exhibited until suddenly a jump occurs. We provide a detailed theoretical description of the jump effect for a general eccentric cylinder. Before the jump, when the cylinder moves along the ramp, we can assume a pure rolling motion. However, it turns out that when the cylinder reaches its jumping position, both the normal and static frictional forces approach zero. Thus, it seems that there will no longer be sufficient force to maintain rolling without slip. In order to have a jump without slipping, we prove that the parameters that characterize the dynamic behavior of the cylinder must belong to some restricted region.