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

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Regular and Chaotic Dynamics, 2015, Volume 20, Issue 5, Pages 605–626
DOI: https://doi.org/10.1134/S1560354715050056 (Mi rcd22)

This article is cited in 30 scientific papers (total in 30 papers)

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

Ivan A. Bizyaev^ab, Alexey V. Borisov^b, Alexey O. Kazakov^ac

^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

Citations (30)

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

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.

Received: 14.08.2015

Bibliographic databases:

Document Type: Article

MSC: 37J60, 37N15, 37G35, 70E18, 70F25, 70H45

Language: English

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

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\pages 605--626

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https://www.mathnet.ru/eng/rcd22

https://www.mathnet.ru/eng/rcd/v20/i5/p605

Translation

Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors
I. A. Bizyaev, A. V. Borisov, A. O. Kazakov
Nelin. Dinam., 2016, 12:2, 263–287

This publication is cited in the following 30 articles:

Anastasiia A. Emelianova, Vladimir I. Nekorkin, “Synchronization and Chaos in Adaptive Kuramoto Networks with Higher-Order Interactions: A Review”, Regul. Chaotic Dyn., 30:1 (2025), 57–75
S. V. Gonchenko, A. S. Gonchenko, A. O. Kazakov, E. A. Samylina, “Smeshannaya dinamika: elementy teorii i primery”, Izvestiya vuzov. PND, 32:6 (2024), 722–765
Alexander A. Kilin, Elena N. Pivovarova, “Dynamics of an Unbalanced Disk with a Single Nonholonomic Constraint”, Regul. Chaotic Dyn., 28:1 (2023), 78–106
D.S. Shchapin, A.A. Emelianova, V.I. Nekorkin, “A chaotic oscillation generator based on mixed dynamics of adaptively coupled Kuramoto oscillators”, Chaos, Solitons & Fractals, 166 (2023), 112989
Anastasiia A. Emelianova, Vladimir I. Nekorkin, “The Third Type of Chaos in a System of Adaptively Coupled Phase Oscillators with Higher-Order Interactions”, Mathematics, 11:19 (2023), 4024
A.A. Emelianova, V.I. Nekorkin, “The influence of nonisochronism on mixed dynamics in a system of two adaptively coupled rotators”, Chaos, Solitons & Fractals, 169 (2023), 113271
A. J. Maciejewski, M. Przybylska, “Gyrostatic Suslov Problem”, Rus. J. Nonlin. Dyn., 18:4 (2022), 609–627
Gonchenko S.V., “Three Forms of Dynamical Chaos”, Radiophys. Quantum Electron., 63:9-10 (2021), 756–775
Emelianova A.A., Nekorkin I V., “Emergence and Synchronization of a Reversible Core in a System of Forced Adaptively Coupled Kuramoto Oscillators”, Chaos, 31:3 (2021), 033102
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
Alexey V. Borisov, Evgeniya A. Mikishanina, “Two Nonholonomic Chaotic Systems. Part I. On the Suslov Problem”, Regul. Chaotic Dyn., 25:3 (2020), 313–322
S. P. Kuznetsov, V. P. Kruglov, A. V. Borisov, “Chaplygin sleigh in the quadratic potential field”, EPL, 132:2 (2020), 20008
V. Chigarev, A. Kazakov, A. Pikovsky, “Kantorovich-Rubinstein-Wasserstein distance between overlapping attractor and repeller”, Chaos, 30:7 (2020)
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
A. A. Emelianova, V. I. Nekorkin, “The third type of chaos in a system of two adaptively coupled phase oscillators”, Chaos, 30:5 (2020)
A. Kazakov, “Merger of a Henon-like attractor with a Henon-like repeller in a model of vortex dynamics”, Chaos, 30:1 (2020), 011105
W. Szuminski, M. Przybylska, “Differential galois integrability obstructions for nonlinear three-dimensional differential systems”, Chaos, 30:1 (2020), 013135
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
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
Shengda Hu, Manuele Santoprete, “Suslov Problem with the Clebsch–Tisserand Potential”, Regul. Chaotic Dyn., 23:2 (2018), 193–211

Citing articles in Google Scholar: Russian citations, English citations
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