Abstract:
The aim of this paper is to introduce the tippedisk to the theoretical mechanics community as a new mechanical-mathematical archetype for friction induced instability phenomena. We discuss the modeling and simulation of the tippedisk, which is an inhomogeneous disk showing an inversion phenomenon similar but more complicated than the tippetop. In particular, several models with different levels of abstraction, parameterizations and force laws are introduced. Moreover, the numerical simulations are compared qualitatively with recordings from a high-speed camera. Unlike the tippetop, the tippedisk has no rotational symmetry, which greatly complicates the three-dimensional nonlinear kinematics. The governing differential equations, which are presented here in full detail, describe all relevant physical effects and serve as a starting point for further research.
Citation:
Simon Sailer, Simon R. Eugster, Remco I. Leine, “The Tippedisk: a Tippetop Without Rotational Symmetry”, Regul. Chaotic Dyn., 25:6 (2020), 553–580
\Bibitem{SaiEugLei20}
\by Simon Sailer, Simon R. Eugster, Remco I. Leine
\paper The Tippedisk: a Tippetop Without Rotational Symmetry
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 6
\pages 553--580
\mathnet{http://mi.mathnet.ru/rcd1084}
\crossref{https://doi.org/10.1134/S1560354720060052}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4184414}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000596572500005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85097231418}
Linking options:
https://www.mathnet.ru/eng/rcd1084
https://www.mathnet.ru/eng/rcd/v25/i6/p553
This publication is cited in the following 11 articles:
Jonas Breuling, Giuseppe Capobianco, Simon R. Eugster, Remco I. Leine, “A nonsmooth RATTLE algorithm for mechanical systems with frictional unilateral constraints”, Nonlinear Analysis: Hybrid Systems, 52 (2024), 101469
Simon Sailer, Remco I. Leine, NODYCON Conference Proceedings Series, Advances in Nonlinear Dynamics, Volume I, 2024, 605
Alexei A. Deriglazov, “An asymmetrical body: Example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect”, Communications in Nonlinear Science and Numerical Simulation, 138 (2024), 108257
Alexander A. Kilin, Elena N. Pivovarova, “Dynamics of an Unbalanced Disk
with a Single Nonholonomic Constraint”, Regul. Chaotic Dyn., 28:1 (2023), 78–106
Jonas Harsch, Simon R. Eugster, “Nonunit quaternion parametrization of a Petrov–Galerkin Cosserat rod finite element”, Proc Appl Math and Mech, 23:4 (2023)
Simon Sailer, Remco I. Leine, “Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory”, Proc. R. Soc. A., 479:2275 (2023)
Alessandro Ciallella, Daria Scerrato, Mario Spagnuolo, Ivan Giorgio, “A continuum model based on Rayleigh dissipation functions to describe a Coulomb-type constitutive law for internal friction in woven fabrics”, Z. Angew. Math. Phys., 73:5 (2022)
Simon R. Eugster, Advanced Structured Materials, 152, Evaluation of Scientific Sources in Mechanics, 2022, 99
S. Sailer, R. I. Leine, “Singularly perturbed dynamics of the tippedisk”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 477:2256 (2021), 20210536
G. Capobianco, J. Harsch, S. R. Eugster, R. I. Leine, “A nonsmooth generalized-alpha method for mechanical systems with frictional contact”, Int. J. Numer. Methods Eng., 122:22 (2021), 6497–6526
S. Sailer, R. I. Leine, “Model reduction of the tippedisk: a path to the full analysis”, Nonlinear Dyn., 105:3 (2021), 1955–1975
Citation in format AMSBIB
Contact us: