Spin reversal of the rattleback: theory and experiment

Abstract

The behaviour of a top known variously as the rattleback, celt or wobblestone is studied. When spun on a flat, smooth, horizontal surface, self-induced oscillations about a horizontal axis eventually consume the initial spin energy; once the spinning has ceased, the oscillations decay and the body spins in the opposite direction. Many rattlebacks seem to be spin biased, reversing spin direction only once and only if the initial spin has the proper sense; others reverse readily from either initial spin direction. Analysis and simulation papers appearing over the past century have attempted, respectively, to explain and qualitatively predict the top’s possible behaviours, and to reconcile observed behaviour with various numerical models. In this work, the two broad theories proposed to explain the spin bias, one which neglects slipping and dissipation and one which incorporates these effects, are critically investigated by several means. The validity of the no-slip assumption is questioned. A numerical model which allows for aerodynamic effects and dry friction due to spinning and slipping is developed. The complicated equations of the numerical model are simplified by analysing the transfer of energy between the spin and oscillations. A comprehensive explanation of the behaviour based on this simplified spin model and the realistic limits of the no-slip motion is proposed. Finally, the predictions of the ‘complete’ numerical model and the simplified model are compared with experimental data.