Dynamics of a Wobblestone Lying on Vibrating Platform Modified by Magnetic Interactions

Abstract

Mathematical model of the rattleback is developed, where a special attention is payed to realistic and numerically effective modelling of the contact forces – friction forces and rolling resistance. In particular, special approximations of the resultant friction force and moment for non-point contact area are developed and applied. These reduced models allow to avoid necessity of use of the space discretization near the contact. The rattleback dynamics – regular and chaotic - is investigated numerically in the case of vibrations of the platform on which the object is located. Moreover, the interaction between a pair of magnets - the first situated inside the wobblestone and the second inside the platform – is modelled. The influence of the magnetic force on the system dynamics is investigated – especially in the context of possible use of the rattleback as energy harvesting system.