Vibrations of Euler's disk.
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.