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

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