If a coin is spun on a table, then we observe a peculiar kind of motion. After a brief initial phase, the coin wobbles/spins while remaining on more or less the same spot. Very slowly the coin loses height. This motion is accompanied by a ringing noise of which the frequency is rapidly increasing and tends to infinity before the motion and sound abruptly stop. This phenomenon is exemplified by the ‘Euler disk’, a scientific toy consisting of a heavy metal disk on a slightly concave mirror. The abrupt halt of a spinning disk is often called the ‘finite-time singularity’.

Another spinning toy which is in frictional contact with a support is the Tippetop. The Tippetop consists of a spherical body with a stick on top. If the top is not in motion, then its stick stands right-up. If we rotate the top very fastly, then the top slowly inverts its orientation and the toy turns a while on its stick. The inversion of the top is due to a friction induced gyroscopic moment.

In this research project a combined experimental, theoretical and numerical investigation is conducted of the complicated dynamics of three-dimensional spinning objects with frictional contact. The motion of the ‘Euler disk’ and the Tippetop are recorded with a high-speed camera and analysed with tailored video imaging techniques. The combined experimental/ theoretical approach indicates that the dominant dissipation mechanism for the finite-time singularity of the Euler disk is due to contour (rolling) friction.

Experimental anaylsis of the Euler disk: setup (left) and image processing (right)

Analysis of the Tippetop: setup (left) and numerical simulation (right)

Publications:

Leine, R.I., "Experimental and theoretical investigation of the energy dissipation of a rolling disk during its final stage of motion", Archive of Applied Mechanics, Vol. 79, No. 11, pp.1063-1082, 2009. PDF (743kb)

Le Saux, C., Leine, R.I. and Glocker, Ch., "Dynamics of a rolling disk in the presence of dry friction", Journal of Nonlinear Science, Vol. 15, No 1, pp. 27-61, 2005. PDF(1426kb)

Leine, R.I. and Glocker, Ch., "A set-valued force law for spatial Coulomb-Contensou friction", European Journal of Mechanics, Vol. 22,2, pp. 193-216, 2003. PDF(421kb)

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09/12/11 | Remco Leine | ZfM | ETH