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Regul. Chaotic Dyn., 2015, Volume 20, Issue 5, Pages 605–626 (Mi rcd22)  

This article is cited in 21 scientific papers (total in 21 papers)

Dynamics of the Suslov Problem in a Gravitational Field: Reversal and Strange Attractors

Ivan A. Bizyaevab, Alexey V. Borisovb, Alexey O. Kazakovac

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
c National Research University Higher School of Economics, ul. Rodionova 136, Nizhny Novgorod, 603093 Russia

Abstract: In this paper, we present some results on chaotic dynamics in the Suslov problem which describe the motion of a heavy rigid body with a fixed point, subject to a nonholonomic constraint, which is expressed by the condition that the projection of angular velocity onto the body-fixed axis is equal to zero. Depending on the system parameters, we find cases of regular (in particular, integrable) behavior and detect various attracting sets (including strange attractors) that are typical of dissipative systems. We construct a chart of regimes with regions characterizing chaotic and regular regimes depending on the degree of conservativeness. We examine in detail the effect of reversal, which was observed previously in the motion of rattlebacks.

Keywords: Suslov problem, nonholonomic constraint, reversal, strange attractor

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
15-12-20035
Russian Foundation for Basic Research 15-38-20879 mol_a_ved
15-08-09261-a
Sections 1, 3 and 7 were prepared by A.V. Borisov under the RSF grant No. 14-50-00005. Sections 2 and 5 were prepared by I.A. Bizyaev within the framework of the RFBR grants No. 15-38-20879 mol_a_ved and No. 15-08-09261-a. The work of A.O. Kazakov (Sections 4 and 6) was supported by RSF grant No. 15-12-20035.


DOI: https://doi.org/10.1134/S1560354715050056

References: PDF file   HTML file

Bibliographic databases:

MSC: 37J60, 37N15, 37G35, 70E18, 70F25, 70H45
Received: 14.08.2015
Language:

Citation: Ivan A. Bizyaev, Alexey V. Borisov, Alexey O. Kazakov, “Dynamics of the Suslov Problem in a Gravitational Field: Reversal and Strange Attractors”, Regul. Chaotic Dyn., 20:5 (2015), 605–626

Citation in format AMSBIB
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\by Ivan A. Bizyaev, Alexey V. Borisov, Alexey O. Kazakov
\paper Dynamics of the Suslov Problem in a Gravitational Field: Reversal and Strange Attractors
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 5
\pages 605--626
\mathnet{http://mi.mathnet.ru/rcd22}
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    Translation

    This publication is cited in the following articles:
    1. A. Nanda, P. Singla, M. F. Karami, “Energy harvesting using rattleback: theoretical analysis and simulations of spin resonance”, Journal of Sound and Vibration, 369 (2016), 195–208  crossref  isi  scopus
    2. Alexey V. Borisov, Ivan S. Mamaev, “Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 232–248  mathnet  crossref  mathscinet  zmath  elib
    3. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “The Hess–Appelrot system and its nonholonomic analogs”, Proc. Steklov Inst. Math., 294 (2016), 252–275  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. 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
    5. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Istoriko-kriticheskii obzor razvitiya negolonomnoi mekhaniki: klassicheskii period”, Nelineinaya dinam., 12:3 (2016), 385–411  mathnet  crossref  zmath  elib
    6. Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Historical and Critical Review of the Development of Nonholonomic Mechanics: the Classical Period”, Regul. Chaotic Dyn., 21:4 (2016), 455–476  mathnet  crossref
    7. S. P. Kuznetsov, V. P. Kruglov, “On some simple examples of mechanical systems with hyperbolic chaos”, Proc. Steklov Inst. Math., 297 (2017), 208–234  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Stefan Rauch-Wojciechowski, Maria Przybylska, “Understanding Reversals of a Rattleback”, Regul. Chaotic Dyn., 22:4 (2017), 368–385  mathnet  crossref
    9. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. A. S. Gonchenko, S. V. Gonchenko, A. O. Kazakov, D. V. Turaev, “On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators”, Physica D, 350 (2017), 45–57  crossref  mathscinet  zmath  isi  scopus
    11. Shengda Hu, Manuele Santoprete, “Suslov Problem with the Clebsch–Tisserand Potential”, Regul. Chaotic Dyn., 23:2 (2018), 193–211  mathnet  crossref
    12. 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  mathnet  crossref  mathscinet
    13. A. O. Kazakov, “On the appearance of mixed dynamics as a result of collision of strange attractors and repellers in reversible systems”, Radiophys. Quantum Electron., 61:8-9 (2019), 650–658  crossref  isi  scopus
    14. S. V. Gonchenko, A. S. Gonchenko, A. O. Kazakov, “Three Types of Attractors and Mixed Dynamics of Nonholonomic Models of Rigid Body Motion”, Proc. Steklov Inst. Math., 308 (2020), 125–140  mathnet  crossref  crossref  mathscinet  isi  elib
    15. Alexey V. Borisov, Evgeniya A. Mikishanina, “Two Nonholonomic Chaotic Systems. Part I. On the Suslov Problem”, Regul. Chaotic Dyn., 25:3 (2020), 313–322  mathnet  crossref  mathscinet
    16. S. P. Kuznetsov, V. P. Kruglov, A. V. Borisov, “Chaplygin sleigh in the quadratic potential field”, EPL, 132:2 (2020), 20008  crossref  isi  scopus
    17. V. Chigarev, A. Kazakov, A. Pikovsky, “Kantorovich-Rubinstein-Wasserstein distance between overlapping attractor and repeller”, Chaos, 30:7 (2020)  crossref  mathscinet  zmath  isi  scopus
    18. I. A. Bizyaev, I. S. Mamaev, “Dynamics of the nonholonomic Suslov problem under periodic control: unbounded speedup and strange attractors”, J. Phys. A-Math. Theor., 53:18 (2020), 185701  crossref  mathscinet  isi  scopus
    19. A. A. Emelianova, V. I. Nekorkin, “The third type of chaos in a system of two adaptively coupled phase oscillators”, Chaos, 30:5 (2020)  crossref  mathscinet  zmath  isi  scopus
    20. A. Kazakov, “Merger of a Henon-like attractor with a Henon-like repeller in a model of vortex dynamics”, Chaos, 30:1 (2020), 011105  crossref  mathscinet  zmath  isi  scopus
    21. W. Szuminski, M. Przybylska, “Differential galois integrability obstructions for nonlinear three-dimensional differential systems”, Chaos, 30:1 (2020), 013135  crossref  mathscinet  zmath  isi  scopus
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