Euler's disk: examples used in engineering and applied mathematics teaching

Euler's disk is a toy described at http://www.eulersdisk.com. Aspects of its motion are modelled as an ideal disk rolling on a horizontal plane. In the final stages of Euler disk motions, the disk is nearly flat to the plane. Asymptotic approximations to the frequency of finite amplitude oscillations on steady (non-dissipative) rolling motions of the Euler disk are described. There are two different approximations which are appropriate in different limits. When the parameters are such that both apply, the formulae for the frequency agree: this appears to be new and simple. The material has been used in teaching; the teaching, and related, materials are available via the web [Keady, Math2200 Lecture Handouts, UWA].