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Эта публикация цитируется в 14 научных статьях (всего в 14 статьях)
Spiral Chaos in the Nonholonomic Model of a Chaplygin Top
Alexey V. Borisova, Alexey O. Kazakovb, Igor R. Sataevac
a Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034 Russia
b National Research University Higher School of Economics,
ul. Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155 Russia
c Institute of Radio Engineering and Electronics RAS, Saratov Branch
ul. Zelenaya 38, Saratov, 410019 Russia
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.
Ключевые слова:
nonholonomic constraint, spiral chaos, discrete spiral attractor
| Финансовая поддержка |
Номер гранта |
Российский фонд фундаментальных исследований  |
15-08-09261-a
14-01-00344 |
| Министерство образования и науки Российской Федерации |
98 |
| Российский научный фонд |
15-12-20035 |
| Фонд Дмитрия Зимина «Династия» |
|
| 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. |
DOI:
https://doi.org/10.1134/S1560354716070157
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Тип публикации:
Статья
MSC: 37J60, 37N15, 37G35, 70E18, 70F25, 70H45
Поступила в редакцию: 12.10.2016
Принята в печать:29.11.2016
Язык публикации: английский
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
Цитирование в формате AMSBIB
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\paper Spiral Chaos in the Nonholonomic Model of a Chaplygin Top
\jour Regul. Chaotic Dyn.
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\vol 21
\issue 7-8
\pages 939--954
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Образцы ссылок на эту страницу:
http://mi.mathnet.ru/rcd238 http://mi.mathnet.ru/rus/rcd/v21/i7/p939
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
-
Alexey V. Borisov, Alexey O. Kazakov, Elena N. Pivovarova, “Regular and Chaotic Dynamics in the Rubber Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 885–901
 -
S. P. Kuznetsov, “Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint”, EPL, 118:1 (2017), 10007
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А. Д. Козлов, “Примеры странных аттракторов в трехмерных неориентируемых отображениях”, Журнал СВМО, 19:2 (2017), 62–75
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А. В. Борисов, А. О. Казаков, Е. Н. Пивоварова, “Регулярная и хаотическая динамика в «резиновой» модели волчка Чаплыгина”, Нелинейная динам., 13:2 (2017), 277–297
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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
-
V. Putkaradze, S. Rogers, “On the dynamics of a rolling ball actuated by internal point masses”, Meccanica, 53:15 (2018), 3839–3868
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A. S. Conchenko, V S. Conchenko, V O. 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
-
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
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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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A. S. Gonchenko, S. V. Gonchenko, A. O. Kazakov, E. A. Samylina, “Chaotic dynamics and multistability in the nonholonomic model of a celtic stone”, Radiophys. Quantum Electron., 61:10 (2019), 773–786
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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
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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)
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