Rattleback’s Chaotic Oscillations

Abstract

The rattleback is a canoe-shaped object with the curious property of spin asymmetry. It provides a prototype of chiral dynamics, wherein lack of mirror-symmetry leads to unconventional dynamics. In this paper dynamics of rattleback are introduced and by applying Kane’s model, it is shown that one can construct a realistic mathematical model by assuming rolling without slipping and employing a torque proportional to angular velocity, in order to provide for energy dissipation. Time series analysis is performed following Grassberger–Procaccia method. The time series corresponds to the dependence of yaw, roll and spin angles on time and their corresponding angular velocities. Finally, rattleback’s strange attractor’s invariant parameters as correlation and minimum embedding dimension, Kolmogorov entropy and Lyapunov exponents, are calculated.