Nonholonomic dynamical systems and the Strange Attractors in the Rattleback

Alexey Boriosv and Ivan Mamaev
Institute of Computer Science, Udmurt State University

We consider different types of behavior of nonholonomic dynamical systems depending on the presence of tensor invariants (hierarchy of dynamics). Some new cases of existence of additional integrals and invariant measure are discussed. Obstacles for nonholonomic systems to be Hamiltonian are investigated.

Also we present some interesting results of computer analysis of the Rattleback dynamics (a nonholonomic problem) and discuss the possibility for existence of strange attractors in such systems. Numerical analysis was performed using the three-dimensional Poincaré section technique.