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.
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Funding
The work of A. V. Borisov (Introduction, Section 1 and Section 4) was supported by RFBR grant 18-29-10051_mk and was carried out at MIPT under project 5–100 for state support for leading universities of the Russian Federation. The work of E. A. Mikishanina (Section 2 and Section 3) was supported by the Russian Science Foundation (project no. 19-71-30012).
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Borisov, A.V., Mikishanina, E.A. Two Nonholonomic Chaotic Systems. Part I. On the Suslov Problem. Regul. Chaot. Dyn. 25, 313–322 (2020). https://doi.org/10.1134/S1560354720030065
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DOI: https://doi.org/10.1134/S1560354720030065