This article is cited in 4 papers

Two Nonholonomic Chaotic Systems. Part I. On the Suslov Problem

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

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

Abstract: A generalization of the Suslov problem with changing parameters is considered. The physical interpretation is a Chaplygin sleigh moving on a sphere. The problem is reduced to the study of a two-dimensional system describing the evolution of the angular velocity of a body. The system without viscous friction and the system with viscous friction are considered. Poincaré maps are constructed, attractors and noncompact attracting trajectories are found. The presence of noncompact trajectories in the Poincaré map suggests that acceleration is possible in this nonholonomic system. In the case of a system with viscous friction, a chart of dynamical regimes and a bifurcation tree are constructed to analyze the transition to chaos. The classical scenario of transition to chaos through a cascade of period doubling is shown, which may indicate attractors of Feigenbaum type.

Keywords: Suslov problem, nonholonomic system, Poincaré map, attractor, noncompact trajectory.

MSC: 37J60, 70E55

Received: 30.03.2020
Accepted: 29.04.2020

Language: English

DOI: 10.1134/S1560354720030065

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