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-65–417 Zielona Góra, Poland
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.
rattleback, rigid body dynamics, nonholonomic mechanics, numerical solutions
|National Science Centre (Narodowe Centrum Nauki)
|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.
MSC: 37J60, 37J25, 70G45
Stefan Rauch-Wojciechowski, Maria Przybylska, “Understanding Reversals of a Rattleback”, Regul. Chaotic Dyn., 22:4 (2017), 368–385
Citation in format AMSBIB
\by Stefan Rauch-Wojciechowski, Maria Przybylska
\paper Understanding Reversals of a Rattleback
\jour Regul. Chaotic Dyn.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
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
|Number of views:|