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Regular and Chaotic Dynamics, 2002, Volume 7, Issue 1, Pages 49–60
DOI: https://doi.org/10.1070/RD2002v007n01ABEH000195
(Mi rcd802)
 

This article is cited in 48 scientific papers (total in 48 papers)

Nonholonomic Systems

The Ringing of Euler's Disk

P. Kessler, O. M. O'Reilly

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, California 94720-1740, U.S.A.
Citations (48)
Abstract: The motion of disks spun on tables has the well-known feature that the associated acoustic signal increases in frequency as the motion tends towards its abrupt halt. Recently, a commercial toy, known as Euler's disk, was designed to maximize the time before this abrupt ending. In this paper, we present and simulate a rigid body model for Euler's disk. Based on the nature of the contact force between the disk and the table revealed by the simulations, we conjecture a new mechanism for the abrupt halt of the disk and the increased acoustic frequency associated with the decline of the disk.
Received: 23.01.2002
Bibliographic databases:
Document Type: Personalia
MSC: 70E18, 70E40
Language: English
Citation: P. Kessler, O. M. O'Reilly, “The Ringing of Euler's Disk”, Regul. Chaotic Dyn., 7:1 (2002), 49–60
Citation in format AMSBIB
\Bibitem{KesOre02}
\by P. Kessler, O. M. O'Reilly
\paper The Ringing of Euler's Disk
\jour Regul. Chaotic Dyn.
\yr 2002
\vol 7
\issue 1
\pages 49--60
\mathnet{http://mi.mathnet.ru/rcd802}
\crossref{https://doi.org/10.1070/RD2002v007n01ABEH000195}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1900054}
\zmath{https://zbmath.org/?q=an:1013.70005}
Linking options:
  • https://www.mathnet.ru/eng/rcd802
  • https://www.mathnet.ru/eng/rcd/v7/i1/p49
  • This publication is cited in the following 48 articles:
    1. E Aldo Arroyo, M Aparicio Alcalde, “Jump effect of an eccentric cylinder rolling on an inclined plane”, J. Phys. A: Math. Theor., 57:3 (2024), 035701  crossref
    2. Theresa E. Honein, Oliver M. O'Reilly, “On the dynamics of transporting rolling cylinders”, Nonlinear Dyn, 2024  crossref
    3. Alexander A. Kilin, Elena N. Pivovarova, “Dynamics of an Unbalanced Disk with a Single Nonholonomic Constraint”, Regul. Chaotic Dyn., 28:1 (2023), 78–106  mathnet  crossref  mathscinet
    4. Yifan Liu, “On the dynamics of rotating rigid tube and its interaction with air”, Math. Model. Nat. Phenom., 18 (2023), 31  crossref
    5. Simon Sailer, Remco I. Leine, “Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory”, Proc. R. Soc. A., 479:2275 (2023)  crossref
    6. Sailer S. Leine R.I., “Singularly Perturbed Dynamics of the Tippedisk”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 477:2256 (2021), 20210536  crossref  mathscinet  isi
    7. Sailer S. Leine R.I., “Model Reduction of the Tippedisk: a Path to the Full Analysis”, Nonlinear Dyn., 105:3 (2021), 1955–1975  crossref  isi  scopus
    8. Darmendrail L., Mueller A., “The Euler Disk and Its Dynamic Finite Time Singularity: Investigating a Fascinating Acoustical and Mechanical Phenomenon With Simple Means”, Acoust. Sci. Technol., 42:4 (2021), 193–199  crossref  isi  scopus
    9. Simon Sailer, Simon R. Eugster, Remco I. Leine, “The Tippedisk: a Tippetop Without Rotational Symmetry”, Regul. Chaotic Dyn., 25:6 (2020), 553–580  mathnet  crossref  mathscinet
    10. Volkel S., Huang K., “Coupling Between Rotational and Translational Motions of a Vibrated Polygonal Disk”, New J. Phys., 22:12 (2020), 123018  crossref  isi  scopus
    11. Takan H. Takatori S. Ichino T., “Continuous Rolling Motion of a Disk on a Vibrating Plate”, Nonlinear Dyn., 100:3 (2020), 2205–2214  crossref  isi  scopus
    12. Martins Flavius Portella Ribas Fleury Agenor de Toledo Trigo F.C., “Motion of a Disk in Contact With a Parametric 2D Curve and Painleve'S Paradox”, Multibody Syst. Dyn., 48:4 (2020), 427–450  crossref  mathscinet  zmath  isi  scopus
    13. Bronars A. O'Reilly O.M., “Gliding Motions of a Rigid Body: the Curious Dynamics of Littlewood'S Rolling Hoop”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 475:2231 (2019), 20190440  crossref  mathscinet  isi
    14. Cross R., “The Abrupt Ending of a Spinning Disk”, Eur. J. Phys., 40:6 (2019), 065002  crossref  isi  scopus
    15. A. S. Sumbatov, “On rolling of a heavy disk on a surface of revolution with negative curvature”, Mech. Sol., 54:5 (2019), 638–651  crossref  crossref  isi  elib  scopus
    16. Natsiavas S., “Analytical Modeling of Discrete Mechanical Systems Involving Contact, Impact, and Friction”, Appl. Mech. Rev., 71:5, SI (2019), 050802  crossref  isi  scopus
    17. Alexander A. Kilin, Elena N. Pivovarova, “Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 23:7-8 (2018), 887–907  mathnet  crossref  mathscinet
    18. S Alaci, F-C Ciornei, I-C Romanu, M-C Ciornei, “Evaluation of spinning friction from a thrust ball bearing”, IOP Conf. Ser.: Mater. Sci. Eng., 400 (2018), 022002  crossref
    19. Rod Cross, “Effects of rolling friction on a spinning coin or disk”, Eur. J. Phys., 39:3 (2018), 035005  crossref
    20. Alexander A. Kilin, Elena N. Pivovarova, “The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane”, Regul. Chaotic Dyn., 22:3 (2017), 298–317  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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