This article is cited in 10 papers

Understanding Reversals of a Rattleback

Stefan Rauch-Wojciechowski^a, Maria Przybylska<sup>b

a</sup> Department of Mathematics, Linköping University, 581 83 Linköping, Sweden
^b Institute of Physics, University of Zielona Góra, Licealna 9, PL-65–417 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.

MSC: 37J60, 37J25, 70G45

Received: 01.06.2017
Accepted: 19.06.2017

Language: English

DOI: 10.1134/S1560354717040037

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