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Regul. Chaotic Dyn., 2017, Volume 22, Issue 4, Pages 368–385 (Mi rcd261)  

This article is cited in 1 scientific paper (total in 1 paper)

Understanding Reversals of a Rattleback

Stefan Rauch-Wojciechowskia, Maria Przybylskab

a Department of Mathematics, Linköping University, 581 83 Linköping, Sweden
b Institute of Physics, University of Zielona Góra, Licealna 9, PL-65417 Zielona Góra, Poland

Abstract: A counterintuitive unidirectional (say counterclockwise) motion of a toy rattleback takes place when it is started by tapping it at a long side or by spinning it slowly in the clockwise sense of rotation. We study the motion of a toy rattleback having an ellipsoidal-shaped bottom by using frictionless Newton equations of motion of a rigid body rolling without sliding in a plane. We simulate these equations for tapping and spinning initial conditions to see the contact trajectory, the force arm and the reaction force responsible for torque turning the rattleback in the counterclockwise sense of rotation. Long time behavior of such a rattleback is, however, quasi-periodic and a rattleback starting with small transversal oscillations turns in the clockwise direction.

Keywords: rattleback, rigid body dynamics, nonholonomic mechanics, numerical solutions

Funding Agency Grant Number
National Science Centre (Narodowe Centrum Nauki) DEC-2013/09/B/ST1/04130
M. P. has been supported by grant No. DEC-2013/09/B/ST1/04130 of the National Science Center of Poland. S. R. and M.P. gratefully acknowledge support of the Department of Mathematics of Linköping University for this work and for M. P. visit in Linköping.


DOI: https://doi.org/10.1134/S1560354717040037

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 37J60, 37J25, 70G45
Received: 01.06.2017
Accepted:19.06.2017
Language: English

Citation: Stefan Rauch-Wojciechowski, Maria Przybylska, “Understanding Reversals of a Rattleback”, Regul. Chaotic Dyn., 22:4 (2017), 368–385

Citation in format AMSBIB
\Bibitem{RauPrz17}
\by Stefan Rauch-Wojciechowski, Maria Przybylska
\paper Understanding Reversals of a Rattleback
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 4
\pages 368--385
\mathnet{http://mi.mathnet.ru/rcd261}
\crossref{https://doi.org/10.1134/S1560354717040037}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000407398500003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85026865145}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
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