A prototype of a spherical tippe top

Abstract

Among spinning objects, the tippe top exhibits one of the most bizarre and counterintuitive behaviours. The commercially available tippe tops basically consist of a section of a sphere with a rod. After spinning on its rounded body, the top flips over and continues spinning on the stem. It is the friction with the bottom surface and the position of the center of mass below the centre of curvature that cause the tippe top to rise its centre of mass while continuing rotating around its symmetry axis (through the stem). The commonly used simplified mathematical model for the tippe top is a sphere whose mass distribution is axially but not spherically symmetric, spinning on a flat surface subject to a small friction force that is due to sliding. According to the eccentricity of the sphere and the Jellet invariant (which includes information on the initial angular velocity) three main different dynamical behaviours are distinguished: tipping, non-tipping, hanging (i.e. the top rises but converges to an intermediate state instead of rising all the way to the vertical state.). Subclasses according to the stability of relative equilibria can further be distinguished. Our concern is the quantitative verification of the mathematical model. We applied 3D-printing to manufacture a '3-in-1 toy' that could catch the three main characteristics defining the three main groups in the classification of spherical tippe tops as mentioned above. This 'toy' allows verification by experimentation.