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Regul. Chaotic Dyn., 2016, Volume 21, Issue 7-8, Pages 792–803 (Mi rcd225)  

This article is cited in 10 scientific papers (total in 10 papers)

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

Abstract: 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.

Keywords: Chaplygin sleigh, nonholonomic mechanics, attractor, chaos, bifurcation

Funding Agency Grant Number
Russian Science Foundation 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

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Bibliographic databases:

Document Type: Article
MSC: 37J60, 37C10, 34D45, 37E30, 34C60
Received: 26.10.2016
Accepted:05.12.2016
Language: English

Citation: 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

Citation in format AMSBIB
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\by Alexey V. Borisov, Sergey P. Kuznetsov
\paper Regular and Chaotic Motions of a Chaplygin Sleigh under Periodic Pulsed Torque Impacts
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 792--803
\mathnet{http://mi.mathnet.ru/rcd225}
\crossref{https://doi.org/10.1134/S1560354716070029}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref
    2. 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  mathnet  crossref
    3. Alexey V. Borisov, Ivan S. Mamaev, “An Inhomogeneous Chaplygin Sleigh”, Regul. Chaotic Dyn., 22:4 (2017), 435–447  mathnet  crossref  mathscinet
    4. 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  mathnet  crossref
    5. I. A. Bizyaev, A. V. Borisov, S. P. Kuznetsov, “Chaplygin sleigh with periodically oscillating internal mass”, EPL, 119:6 (2017), 60008  crossref  isi
    6. S. P. Kuznetsov, “Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint”, EPL, 118:1 (2017), 10007  crossref  mathscinet  isi  scopus
    7. A. V. Borisov, I. S. Mamaev, “Neodnorodnye sani Chaplygina”, Nelineinaya dinam., 13:4 (2017), 625–639  mathnet  crossref  elib
    8. V. Fedonyuk, Ph. Tallapragada, “Sinusoidal control and limit cycle analysis of the dissipative chaplygin sleigh”, Nonlinear Dyn., 93:2 (2018), 835–846  crossref  isi  scopus
    9. 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  mathnet  crossref
    10. 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  mathnet  crossref
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