The problem of rolling a nonholonomic bundle of two bodies is considered:
a spherical shell with a rigid body rotating along the axis of symmetry, on which rotors spinning
relative to this body are fastened. This problem can be regarded as a distant generalization of the
Chaplygin ball problem. The reduced system is studied by analyzing Poincaré maps constructed
in Andoyer – Deprit variables. A classification of Poincaré maps of the reduced system is carried
out, the behavior of the contact point is studied, and the cases of chaotic oscillations of the
system are examined in detail. To study the nature of the system’s chaotic behavior, a map of
dynamical regimes is constructed. The Feigenbaum type of attractor is shown.
Keywords:
nonholonomic system, Poincaré map, strange attractor, chart of dynamical regimes
Citation:
Borisov A. V., Mikishanina E. A., Two Nonholonomic Chaotic Systems. Part II. On the Rolling of a Nonholonomic Bundle of Two Bodies, Regular and Chaotic Dynamics,
2020, Volume 25, Number 4,
pp. 392-400