Abstract:
We present a qualitative analysis of the dynamics of a rolling and sliding disk in a horizontal plane. It is based on using three classes of asymptotic solutions: straight-line rolling, spinning about a vertical diameter and tumbling solutions. Their linear stability analysis is given and it is complemented with computer simulations of solutions starting in the vicinity of the asymptotic solutions. The results on asymptotic solutions and their linear stability apply also to an annulus and to a hoop.
Keywords:
rigid body, nonholonomic mechanics, rolling disk, sliding disk.
M.P. has been supported by grant No. DEC-2013/09/B/ST1/04130 of the National Science Center of Poland, and M.P. and S.R. gracefully acknowledge support from the Department of Mathematics of Linköping University.
Citation:
Maria Przybylska, Stefan Rauch-Wojciechowski, “Dynamics of a Rolling and Sliding Disk in a Plane. Asymptotic Solutions, Stability and Numerical Simulations”, Regul. Chaotic Dyn., 21:2 (2016), 204–231
\Bibitem{PrzRau16}
\by Maria Przybylska, Stefan Rauch-Wojciechowski
\paper Dynamics of a Rolling and Sliding Disk in a Plane. Asymptotic Solutions, Stability and Numerical Simulations
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 2
\pages 204--231
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https://www.mathnet.ru/eng/rcd75
https://www.mathnet.ru/eng/rcd/v21/i2/p204
This publication is cited in the following 6 articles:
A. G. Agúndez, D. García-Vallejo, E. Freire, “Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints”, Nonlinear Dyn, 112:4 (2024), 2453
Stefan Rauch-Wojciechowski, Maria Przybylska, “On Dynamics of Jellet's Egg. Asymptotic Solutions Revisited”, Regul. Chaotic Dyn., 25:1 (2020), 40–58
Simon Sailer, Simon R. Eugster, Remco I. Leine, “The Tippedisk: a Tippetop Without Rotational Symmetry”, Regul. Chaotic Dyn., 25:6 (2020), 553–580
F. C. Martins Flavius Portella Ribas Fleury Agenor de Toledo Trigo, “Motion of a disk in contact with a parametric 2D curve and Painleve's paradox”, Multibody Syst. Dyn., 48:4 (2020), 427–450
A. S. Sumbatov, “On rolling of a heavy disk on a surface of revolution with negative curvature”, Mech. Sol., 54:5 (2019), 638–651
A. V. Borisov, A. A. Kilin, Yu. L. Karavaev, “Retrograde motion of a rolling disk”, Phys. Usp., 60:9 (2017), 931–934
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