On the rattleback dynamics

Abstract

In this paper we present some relevant dynamical properties of an idealized conservative model of the rattleback, from the Poisson dynamics point of view. In the first half of the article, along with a dynamical study of the orbits, using a Hamilton-Poisson realization of the dynamical system, we provide a geometric characterization of the space of orbits in terms of Whitney stratifications associated to the image of the energy-Casimir mapping. In the second half of the article we provide an explicit method to stabilize asymptotically any arbitrary fixed orbit/cycle of the rattleback system and to keep unchanged the geometry of the model space.