Strange attractors in rattleback dynamics
A.V. Borisov a
I.S. Mamaev b
a Lomonosov Moscow State University, Vorobevy Gory, Moscow, 119991, Russian Federation
b Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russian Federation
This review is dedicated to the dynamics of the rattleback, a phenomenon with curious physical properties that is studied in nonholonomic mechanics. All known analytical results are collected here, and some results of our numerical simulation are presented. In particular, three-dimensional Poincare maps associated with dynamical systems are systematically investigated for the first time. It is shown that the loss of stability of periodic and quasiperiodic solutions, which gives rise to strange attractors, is typical of the three-dimensional maps related to rattleback dynamics. This explains some newly discovered properties of the rattleback related to the transition from regular to chaotic solutions at certain values of the physical parameters.