rolling, and derived the formula for spin reversal time.

As the first numerical study, Kane and Levinson [@Kane1982] simulated the energy-conserving equations and showed that the rattleback changes its spinning direction indefinitely for certain parameter values and initial conditions. They also demonstrated the coupling between the oscillations and the spinning by showing that it starts to rotate when it begins with pure pitching or rolling, but the direction of the rotation is different between pitching and rolling. Similar simulations were performed by Lindberg and Longman independently [@Lindberg1983]. Nanda *et al.* simulated the spin resonance of the rattleback on a vibrating base [@Nanda2016].

Energy-conserving dynamical systems usually conserve the phase volume, but the present rattleback dynamics does not explore the whole phase volume with a given energy because of a non-holonomic constraint due to the no-slip condition. Therefore, the Liouville theorem does not hold, and such a system has been shown to behave much like dissipative systems. Borisov and Mamaev in fact reported the existence of “strange attractor” for certain parameter values in the present system [@Borisov2003]. The no-slip rattleback system has been actively studied in the context of chaotic dynamics during the last decade [@Borisov2006; @Borisov2014].

Effects of dissipation at 