A. V. Borisov, I. S. Mamaev, “Strange attractors in rattleback dynamics”, UFN, 173:4 (2003), 407–418; Phys. Usp., 46:4 (2003), 393

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Uspekhi Fizicheskikh Nauk, 2003, Volume 173, Number 4, Pages 407–418
DOI: https://doi.org/10.3367/UFNr.0173.200304d.0407 (Mi ufn2129)

This article is cited in 103 scientific papers (total in 105 papers)

METHODOLOGICAL NOTES

Strange attractors in rattleback dynamics

A. V. Borisov, I. S. Mamaev

Institute of Computer Science

Full-text PDF (2247 kB) Citations (105)

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DOI: https://doi.org/10.3367/UFNr.0173.200304d.0407

Abstract: This review is dedicated to the dynamics of the rattleback, a phenomenon with curious physical properties that is studied in nonholonomic mechanics. All known analytical results are collected here, and some results of our numerical simulation are presented. In particular, three-dimensional Poincare maps associated with dynamical systems are systematically investigated for the first time. It is shown that the loss of stability of periodic and quasiperiodic solutions, which gives rise to strange attractors, is typical of the three-dimensional maps related to rattleback dynamics. This explains some newly discovered properties of the rattleback related to the transition from regular to chaotic solutions at certain values of the physical parameters.

Received: June 24, 2002
Revised: December 4, 2002

English version:
Physics–Uspekhi, 2003, Volume 46, Issue 4, Pages 393–403
DOI: https://doi.org/10.1070/PU2003v046n04ABEH001306

Bibliographic databases:

Document Type: Article

PACS: 05.45.-a, 45.10.-b, 45.40.-f

Language: Russian

Citation: A. V. Borisov, I. S. Mamaev, “Strange attractors in rattleback dynamics”, UFN, 173:4 (2003), 407–418; Phys. Usp., 46:4 (2003), 393–403

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/ufn2129

https://www.mathnet.ru/eng/ufn/v173/i4/p407

This publication is cited in the following 105 articles:

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Hiroshi Takano, “Analyzing the Motion of a Washer on a Rod”, Regul. Chaotic Dyn., 28:2 (2023), 227–250
Simon Sailer, Remco I. Leine, “Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory”, Proc. R. Soc. A., 479:2275 (2023)
M. A. Munitsyna, “Celtic stone dynamics on a plane with viscous friction”, Autom. Remote Control, 83:3 (2022), 325–331
Ivan A. Bizyaev, Ivan S. Mamaev, “Permanent Rotations in Nonholonomic Mechanics. Omnirotational Ellipsoid”, Regul. Chaotic Dyn., 27:6 (2022), 587–612
A. S. Kuleshov, E. N. Pikunova, “Analytical research of the hopf bifurcation in the problem of motion of the rattleback”, Vestn. St. Petersbg. Univ., Math., 9:2 (2022), 305–315
Gianni Arioli, Hans Koch, “Some Reversing Orbits for a Rattleback Model”, J Nonlinear Sci, 32:3 (2022)
Garcia-Agundez A. Garcia-Vallejo D. Freire E., “Linearization Approaches For General Multibody Systems Validated Through Stability Analysis of a Benchmark Bicycle Model”, Nonlinear Dyn., 103:1 (2021), 557–580
Sailer S., Leine R.I., “Singularly Perturbed Dynamics of the Tippedisk”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 477:2256 (2021), 20210536
Agundez A.G. Garcia-Vallejo D. Freire E., “Linear Stability Analysis of Nonholonomic Multibody Systems”, Int. J. Mech. Sci., 198 (2021), 106392
Gonchenko S.V., “Three Forms of Dynamical Chaos”, Radiophys. Quantum Electron., 63:9-10 (2021), 756–775
Sailer S., Leine R.I., “Model Reduction of the Tippedisk: a Path to the Full Analysis”, Nonlinear Dyn., 105:3 (2021), 1955–1975
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
Simon Sailer, Simon R. Eugster, Remco I. Leine, “The Tippedisk: a Tippetop Without Rotational Symmetry”, Regul. Chaotic Dyn., 25:6 (2020), 553–580
Bizyaev I.A. Mamaev I.S., “Separatrix Splitting and Nonintegrability in the Nonholonomic Rolling of a Generalized Chaplygin Sphere”, Int. J. Non-Linear Mech., 126 (2020), 103550
Tudoran R.M. Girban A., “On the Rattleback Dynamics”, J. Math. Anal. Appl., 488:1 (2020), 124066
Kuznetsov S.P., Kruglov V.P., Borisov A.V., “Chaplygin Sleigh in the Quadratic Potential Field”, EPL, 132:2 (2020), 20008
Ivan S. Mamaev, Evgeny V. Vetchanin, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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