Аннотация:
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.
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).
Поступила в редакцию: 30.03.2020 Принята в печать: 29.04.2020
Образец цитирования:
Alexey V. Borisov, Evgeniya A. Mikishanina, “Two Nonholonomic Chaotic Systems. Part I. On the Suslov Problem”, Regul. Chaotic Dyn., 25:3 (2020), 313–322
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\jour Regul. Chaotic Dyn.
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Е. А. Микишанина, “Омниколесная реализация задачи Суслова с реономной связью: динамическая модель и управление”, Вестник российских университетов. Математика, 29:147 (2024), 296–308
Evgeniya A. Mikishanina, “Dynamics of the generalized penny-model on the rotating plane”, Eur. Phys. J. B, 96 (2023), 15–8
Е. А. Микишанина, “Динамика качения сферического робота с маятниковым приводом, управляемого сервосвязью Билимовича”, ТМФ, 211:2 (2022), 281–294; E. A. Mikishanina, “Rolling motion dynamics of a spherical robot with a pendulum actuator controlled by the Bilimovich servo-constraint”, Theoret. and Math. Phys., 211:2 (2022), 679–691
Е. А. Микишанина, “Исследование влияния случайных возмущений на динамику системы в задаче Суслова”, Вестн. Томск. гос. ун-та. Матем. и мех., 2021, № 73, 17–29
Цитирование в формате AMSBIB
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