ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Mathematical Modelling and Simulation of the Bifurcational Wobblestone Dynamics

Discontinuity, Nonlinearity, and Complexity 3(2) (2014) 123--132 | DOI:10.5890/DNC.2014.06.002

Jan Awrejcewicz; Grzegorz Kudra

Department of Automation, Biomechanic and Mechatronics, Lodz University of Technology, Lodz Poland

Abstract

The Celtic stone, sometimes also called wobbles tone or rattleback usually is a semi-ellipsoidal solid with a special mass distribution. Most celts lied on aflat and horizontal base, set in rotational motion around a vertical axis can rotate in only one direction. In this work the dynamics of the celt is simulated numerically, but the solid is forced untypically, i.e. it is situated on a harmonically vibrating base. Essential part of the model are approximate functions describing the contact forces, i.e. dry friction forces and rolling resistance. They are based on previous works of the authors, but some modifications of friction model are made, which can be described as a generalization of the earlier used Padé approximants. Periodic, quasiperiodic and chaotic dynamics of a harmonically forced rattleback is found and presented by the use of Poincaré maps and bifurcation diagrams.

Acknowledgments

This paper was financially supported by the National Science Centre of Poland under the grant MAESTRO 2, No. 2012/04/A/ST8/00738, for years 2013-2016.

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