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arXiv · 2207.02048

On some aspects of the dynamics of a ball in a rotating surface of revolution and of the kasamawashi art

Francesco Fassò·Nicola Sansonetto
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Abstract

We study some aspects of the dynamics of the nonholonomic system formed by a heavy homogeneous ball constrained to roll without sliding on a steadily rotating surface of revolution. First, in the case in which the figure axis of the surface is vertical (and hence the system is $\textrm{SO(3)}\times\textrm{SO(2)}$-symmetric) and the surface has a (nondegenerate) maximum at its vertex, we show the existence of motions asymptotic to the vertex and rule out the possibility of blow up. This is done passing to the 5-dimensional $\textrm{SO(3)}$-reduced system. The $\textrm{SO(3)}$-symmetry persists when the figure axis of the surface is inclined with respect to the vertical -- and the system can be viewed as a simple model for the Japanese kasamawashi (turning umbrella) performance art -- and in that case we study the (stability of the) equilibria of the 5-dimensional reduced system.

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Francesco Fassò, Nicola Sansonetto. 2022-07-05. On some aspects of the dynamics of a ball in a rotating surface of revolution and of the kasamawashi art. https://doi.org/10.1134/s1560354722040025

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