Topic
Euler's Disk
About: Euler's Disk is a research topic. Over the lifetime, 15 publications have been published within this topic receiving 245 citations.
Papers
1 Jan 2005
TL;DR: In this paper, a rigid body model for Euler's disk is presented and simulated based on the nature of the contact force between the disk and the table revealed by the simulations.
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.
49 citations
TL;DR: In this paper, the fixed points of the dynamical system describing the rolling motion of a uniform disk or a uniform circular hoop on a rough horizontal plane without dissipation are analyzed.
31 citations
TL;DR: It is shown that Moffatt's recent calculation regarding the viscous dissipation of circulating air underneath a spinning coin overlooked the importance of the finite width of the viscously boundary layer.
Abstract: It is shown that Moffatt's recent calculation regarding the viscous dissipation of circulating air underneath a spinning coin overlooked the importance of the finite width of the viscous boundary layer. Including the enhanced dissipation in the boundary layer gives a larger dissipation from the moving air, and a scaling law of the decay of the coin's angle that is in much better accord with that observed. However, rolling frictional drag with the surface is an additional damping mechanism that could well dominate that from circulating air.
18 citations
TL;DR: A model of a partially deformable Euler disk is presented that allows transverse vibrations to be treated with the techniques of classical analytical mechanics and shows that the increasing audible frequency produced during motion can be directly related to the forcing effect of the reaction and the angular velocity of the contact point.
Abstract: A model of a partially deformable Euler disk is presented that allows transverse vibrations to be treated with the techniques of classical analytical mechanics. The model clearly shows that the increasing audible frequency produced during motion can be directly related to the forcing effect of the reaction and the angular velocity of the contact point. The material of the disk seems to play a role in affecting the intensity and quality of the sound, but not its pitch. Moreover, the friction force grows rapidly with the decline of the disk, thus causing the slipping that is partially responsible for the abrupt end of the motion. The model also supports the conjecture [P. Kessler and O. M. O'Reilly, Regul. Chaotic Dyn. 7, 49 (2002)] that the vibrations themselves contribute to this phenomenon by causing a loss of contact with the surface at small angles of inclination.
16 citations
TL;DR: In this article, an experimental investigation of a round uniform disk rolling on a horizontal surface is presented, where two methods for experimentally determining the loss of contact of the rolling disk from the horizontal surface before its stop are proposed.
Abstract: This paper is an experimental investigation of a round uniform disk rolling on a horizontal surface. Two methods for experimentally determining the loss of contact of the rolling disk from the horizontal surface before its stop are proposed. Results of experiments for disks having different masses and manufactured from different materials are presented. Causes of “microlosses of contact” detected in the processes of motion are discussed.
14 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 1 |
| 2015 | 1 |
| 2012 | 1 |
| 2010 | 2 |
| 2007 | 1 |
| 2006 | 1 |