Strange attractors in rattleback dynamics

A.V. Borisov^a, I.S. Mamaev^b
^aLomonosov Moscow State University, Vorobevy Gory, Moscow, 119991, Russian Federation
^bUdmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russian Federation

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.

PACS: 05.45.−a, 45.10.−b, 45.40.−f (all)
DOI: 10.1070/PU2003v046n04ABEH001306
URL: https://ufn.ru/en/articles/2003/4/c/
Web of Science

000184349400003
Citation: Borisov A V, Mamaev I S "Strange attractors in rattleback dynamics" Phys. Usp. 46 393–403 (2003)

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Оригинал: Борисов А В, Мамаев И С «Странные аттракторы в динамике кельтских камней» УФН 173 407–418 (2003); DOI: 10.3367/UFNr.0173.200304d.0407

References (20) Cited by (78) Similar articles (20) ↓

A.V. Borisov, A.O. Kazakov, S.P. Kuznetsov “Nonlinear dynamics of the rattleback: a nonholonomic model” Phys. Usp. 57 453–460 (2014)
A. Loskutov “Dynamical chaos: systems of classical mechanics” Phys. Usp. 50 939–964 (2007)
A.N. Pavlov, V.S. Anishchenko “Multifractal analysis of complex signals” Phys. Usp. 50 819–834 (2007)
V.I. Klyatskin “Statistical topography and Lyapunov exponents in stochastic dynamical systems” Phys. Usp. 51 395–407 (2008)
O.V. Rudenko “Nonlinear dynamics of quadratically cubic systems” Phys. Usp. 56 683–690 (2013)
S.N. Gordienko “Irreversibility and the probabilistic treatment of the dynamics of classical particles” Phys. Usp. 42 573–590 (1999)
E.N. Rumanov “Critical phenomena far from equilibrium” Phys. Usp. 56 93–102 (2013)
P.S. Landa, Ya.B. Duboshinskii “Self-oscillatory systems with high-frequency energy sources” Sov. Phys. Usp. 32 723–731 (1989)
V.V. Brazhkin “Why does statistical mechanics 'work' in condensed matter?” Phys. Usp. 64 1049–1057 (2021)
E.P. Zemskov “Turing patterns and Newell—Whitehead—Segel amplitude equation” Phys. Usp. 57 1035–1037 (2014)
S.G. Karshenboim “New recommended values of the fundamental physical constants (CODATA 2006)” Phys. Usp. 51 1019–1026 (2008)
A.M. Ignatov, A.I. Korotchenko et al “On the interpretation of computer simulation of classical Coulomb plasma” Phys. Usp. 38 109–114 (1995)
A.A. Kolokolov “Fresnel formulas and the principle of causality” Phys. Usp. 42 931 (1999)
D.A. Shalybkov “Hydrodynamic and hydromagnetic stability of the Couette flow” Phys. Usp. 52 915–935 (2009)
A.V. Kukushkin “A technique for solving the wave equation and prospects for physical applications arising therefrom” Phys. Usp. 36 (2) 81–93 (1993)
V.Yu. Khomich, V.A. Shmakov “Mechanisms of direct laser nanostructuring of materials” Phys. Usp. 58 455–465 (2015)
V.P. Bykov “Basic properties of squeezed light” Sov. Phys. Usp. 34 (10) 910–924 (1991)
G.D. Shabanov “On the possibility of making a natural ball lightning using a new pulse discharge type in the laboratory” Phys. Usp. 62 92–107 (2019)
O.G. Bakunin “Correlation and percolation properties of turbulent diffusion” Phys. Usp. 46 733–744 (2003)
Yu.Yu. Stoilov “Laser beam in a soap film” Phys. Usp. 47 1261–1270 (2004)

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