Аннотация:
This paper presents a numerical study of the chaotic dynamics of a dynamically asymmetric unbalanced ball (Chaplygin top) rolling on a plane. It is well known that the dynamics of such a system reduces to the investigation of a three-dimensional map, which in the general case has no smooth invariant measure. It is shown that homoclinic strange attractors of discrete spiral type (discrete Shilnikov type attractors) arise in this model for certain parameters. From the viewpoint of physical motions, the trace of the contact point of a Chaplygin top on a plane is studied for the case where the phase trajectory sweeps out a discrete spiral attractor. Using the analysis of the trajectory of this trace, a conclusion is drawn about the influence of “strangeness” of the attractor on the motion pattern of the top.
The work of A.V.Borisov (Introduction, Section 2 and Conclusion) was carried out within the
framework of the state assignment for institutions of higher education and supported by the RFBR
grant No. 15-08-09261-a. The work of A.O.Kazakov (Sections 1 and 5) was supported by the Basic
Research Program at the National Research University Higher School of Economics (project 98),
by the Dynasty Foundation, and by the RFBR grant No. 14-01-00344. The work of I.R. Sataev
(Sections 3 and 4) was supported by the RSF grant No. 15-12-20035.
Поступила в редакцию: 12.10.2016 Принята в печать: 29.11.2016
Образец цитирования:
Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Spiral Chaos in the Nonholonomic Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 939–954
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\by Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev
\paper Spiral Chaos in the Nonholonomic Model of a Chaplygin Top
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 939--954
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd238
https://www.mathnet.ru/rus/rcd/v21/i7/p939
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A. S. Gonchenko, M. S. Gonchenko, A. D. Kozlov, E. A. Samylina, “On scenarios of the onset of homoclinic attractors in three-dimensional non-orientable maps”, Chaos, 31:4 (2021), 043122
S. Gonchenko, A. Gonchenko, A. Kazakov, E. Samylina, “On discrete Lorenz-like attractors”, Chaos, 31:2 (2021), 023117
V. Putkaradze, S. Rogers, “On the optimal control of a rolling ball robot actuated by internal point masses”, J. Dyn. Syst. Meas. Control-Trans. ASME, 142:5 (2020)
Vyacheslav P. Kruglov, Sergey P. Kuznetsov, “Topaj – Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators”, Regul. Chaotic Dyn., 24:6 (2019), 725–738
I. R. Garashchuk, D. I. Sinelshchikov, A. O. Kazakov, N. A. Kudryashov, “Hyperchaos and multistability in the model of two interacting microbubble contrast agents”, Chaos, 29:6 (2019), 063131
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С. В. Гонченко, А. С. Гонченко, А. О. Казаков, А. Д. Козлов, Ю. В. Баханова, “Математическая теория динамического хаоса и её приложения: Обзор. Часть 2. Спиральный хаос трехмерных потоков”, Известия вузов. ПНД, 27:5 (2019), 7–52
Ivan R. Garashchuk, Dmitry I. Sinelshchikov, Nikolay A. Kudryashov, “Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall”, Regul. Chaotic Dyn., 23:3 (2018), 257–272
Sergey P. Kuznetsov, “Regular and Chaotic Dynamics of a Chaplygin Sleigh due to Periodic Switch of the Nonholonomic Constraint”, Regul. Chaotic Dyn., 23:2 (2018), 178–192
Pavel V. Kuptsov, Sergey P. Kuznetsov, “Lyapunov Analysis of Strange Pseudohyperbolic Attractors: Angles Between Tangent Subspaces, Local Volume Expansion and Contraction”, Regul. Chaotic Dyn., 23:7-8 (2018), 908–932
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A. S. Conchenko, S. V. Conchenko, O. V. Kazakovt, A. D. Kozlov, “Elements of contemporary theory of dynamical chaos: a tutorial. Part I. Pseudohyperbolic attractors”, Int. J. Bifurcation Chaos, 28:11 (2018), 1830036
S. P. Kuznetsov, “Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint”, EPL, 118:1 (2017), 10007
А. Д. Козлов, “Примеры странных аттракторов в трехмерных неориентируемых отображениях”, Журнал СВМО, 19:2 (2017), 62–75
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