This article is cited in 2 papers

Two Nonholonomic Chaotic Systems. Part II. On the Rolling of a Nonholonomic Bundle of Two Bodies

Alexey V. Borisov^abc, Evgeniya A. Mikishanina<sup>c

a</sup> Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991 Moscow, Russia
^b Moscow Institute of Physics and Technology, Institutskii per. 9, 141700 Dolgoprudnyi, Russia
^c Chuvash State University, Moskovskii pr. 15, 428015 Cheboksary, Russia

Abstract: 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.

MSC: 37J60, 70E55

Received: 11.05.2020
Accepted: 17.06.2020

Language: English

DOI: 10.1134/S1560354720040061

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