On the dynamic behavior of the wobblestone

Abstract

The wobblestone is a generalized form of a top with distinct inertias and a nonspherical surface at the point of contact to the horizontal plane on which it moves. Some wobble-stones exhibit a curious property of allowing steady rotation about the vertical principal inertia axis only when rotated in one direction, while other wobblestones exhibit repeated reversals of the direction of rotation after being spun. Here, nonlinear equations governing the motion of a wobblestone are derived assuming no slippage at the point of contact to the supporting rigid plane, which corresponds to a conservative model. The equations are formulated in a manner suitable for numerical integration. The major observed properties of the motion of these asymmetrical tops are demonstrated in numerical simulations. The results lead to a better understanding of their complex and fundamentally nonlinear motion.