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.
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.
\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}
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This publication is cited in the following 8 articles:
M. A. Munitsyna, “Celtic stone dynamics on a plane with viscous friction”, Autom. Remote Control, 83:3 (2022), 325–331
I. A. Bizyaev, I. S. Mamaev, “Separatrix splitting and nonintegrability in the nonholonomic rolling of a generalized Chaplygin sphere”, Int. J. Non-Linear Mech., 126 (2020), 103550
S. P. Kuznetsov, V. P. Kruglov, A. V. Borisov, “Chaplygin sleigh in the quadratic potential field”, EPL, 132:2 (2020), 20008
R. M. Tudoran, A. Girban, “On the rattleback dynamics”, J. Math. Anal. Appl., 488:1 (2020), 124066
A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Comment on “Confining rigid balls by mimicking quadrupole ion trapping” [Am. J. Phys. 85, 821 (2017)]”, Am. J. Phys., 87:11 (2019), 935–938
S. Jones, H. E. M. Hunt, “Rattlebacks for the rest of us”, Am. J. Phys., 87:9 (2019), 699–713
B. Gajic, B. Jovanovic, “Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere”, Nonlinearity, 32:5 (2019), 1675–1694
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
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