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Эта публикация цитируется в 15 научных статьях (всего в 15 статьях)
Regular and Chaotic Motions of a Chaplygin Sleigh under Periodic Pulsed Torque Impacts
Alexey V. Borisovab, Sergey P. Kuznetsova
a Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Moscow Institute of Physics and Technology,
Institutskii per. 9, Dolgoprudnyi, 141700 Russia
Аннотация:
For a Chaplygin sleigh on a plane, which is a paradigmatic system of nonholonomic mechanics, we consider dynamics driven by periodic pulses of supplied torque depending on the instant spatial orientation of the sleigh. Additionally, we assume that a weak viscous force and moment affect the sleigh in time intervals between the pulses to provide sustained modes of the motion associated with attractors in the reduced three-dimensional phase space (velocity, angular velocity, rotation angle). The developed discrete version of the problem of the Chaplygin sleigh is an analog of the classical Chirikov map appropriate for the nonholonomic situation. We demonstrate numerically, discuss and classify dynamical regimes depending on the parameters, including regular motions and diffusive-like random walks associated, respectively, with regular and chaotic attractors in the reduced momentum dynamical equations.
Ключевые слова:
Chaplygin sleigh, nonholonomic mechanics, attractor, chaos, bifurcation
| Финансовая поддержка |
Номер гранта |
Российский научный фонд  |
15-12-20035 |
| This work was supported by the grant of the Russian Science Foundation No 15-12-20035. |
DOI:
https://doi.org/10.1134/S1560354716070029
 Список литературы:
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Тип публикации:
Статья
MSC: 37J60, 37C10, 34D45, 37E30, 34C60
Поступила в редакцию: 26.10.2016
Принята в печать:05.12.2016
Язык публикации: английский
Образец цитирования:
Alexey V. Borisov, Sergey P. Kuznetsov, “Regular and Chaotic Motions of a Chaplygin Sleigh under Periodic Pulsed Torque Impacts”, Regul. Chaotic Dyn., 21:7-8 (2016), 792–803
Цитирование в формате AMSBIB
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\paper Regular and Chaotic Motions of a Chaplygin Sleigh under Periodic Pulsed Torque Impacts
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\pages 792--803
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Образцы ссылок на эту страницу:
http://mi.mathnet.ru/rcd225 http://mi.mathnet.ru/rus/rcd/v21/i7/p792
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
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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
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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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Alexey V. Borisov, Ivan S. Mamaev, “An Inhomogeneous Chaplygin Sleigh”, Regul. Chaotic Dyn., 22:4 (2017), 435–447
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Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975
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I. A. Bizyaev, A. V. Borisov, S. P. Kuznetsov, “Chaplygin sleigh with periodically oscillating internal mass”, EPL, 119:6 (2017), 60008
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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. В. Борисов, И. С. Мамаев, “Неоднородные сани Чаплыгина”, Нелинейная динам., 13:4 (2017), 625–639
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V. Fedonyuk, Ph. Tallapragada, “Sinusoidal control and limit cycle analysis of the dissipative Chaplygin sleigh”, Nonlinear Dyn., 93:2 (2018), 835–846
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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
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Alexey V. Borisov, Sergey P. Kuznetsov, “Comparing Dynamics Initiated by an Attached Oscillating Particle for the Nonholonomic Model of a Chaplygin Sleigh and for a Model with Strong Transverse and Weak Longitudinal Viscous Friction Applied at a Fixed Point on the Body”, Regul. Chaotic Dyn., 23:7-8 (2018), 803–820
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E. V. Vetchanin, E. A. Mikishanina, “Vibrational Stability of Periodic Solutions of the Liouville Equations”, Нелинейная динам., 15:3 (2019), 351–363
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V A. Borisov , E. V. Vetchanin, I. S. Mamaev, “Motion of a smooth foil in a fluid under the action of external periodic forces. I”, Russ. J. Math. Phys., 26:4 (2019), 412–427
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I. A. Bizyaev, V A. Borisov , V. V. Kozlov, I. S. Mamaev, “Fermi-like acceleration and power-law energy growth in nonholonomic systems”, Nonlinearity, 32:9 (2019), 3209–3233
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B. Gajic, B. Jovanovic, “Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere”, Nonlinearity, 32:5 (2019), 1675–1694
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I. A. Bizyaev, A. V. Borisov, S. P. Kuznetsov, “The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass”, Nonlinear Dyn., 95:1 (2019), 699–714
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