The chiral knife edge: a simplified rattleback to illustrate spin inversion

Abstract

We present the chiral knife edge rattleback, an alternative version of previously presented systems that exhibit spin inversion. We offer a full treatment of the model using qualitative arguments, analytical solutions as well as numerical results. We treat a reduced, one--mode problem which not only contains the essence of the physics of spin inversion, but that also exhibits an unexpected connection to the Chaplygin sleigh, providing new insight into the non-holonomic structure of the problem. We also present exact results for the full problem together with estimates of the time between inversions that agree with previous results in the literature.