Transition of the Bifurcations in the Rotation of a Camphor-Coated Elliptical Paper Disk

An elliptical camphor-coated paper disk whose center of mass is fixed at the rotational axis rotates spontaneously with a constant angular velocity when placed on the surface of water. In our experiments, we observed bifurcation by controlling the water depth, i.e., the disk rotated and was stationary at higher and lower water depths, respectively. Further, the bifurcation type depended on the aspect ratio of the elliptical camphor disk; subcritical and supercritical bifurcations were observed in the high- and low-aspect-ratio experiments, respectively. Thus, the experiments and phenomenological models indicated that the friction between the acrylic rod as the rotational axis and the center pore of the disk penetrated by the rod determined the bifurcation type.