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We study some aspects of the dynamics of the nonholonomic system formed by aheavy homogeneous ball constrained to roll without sliding on a steadilyrotating surface of revolution. First, in the case in which the figure axis ofthe 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 motionsasymptotic to the vertex and rule out the possibility of blow up. This is donepassing to the 5-dimensional $\textrm{SO(3)}$-reduced system. The$\textrm{SO(3)}$-symmetry persists when the figure axis of the surface isinclined with respect to the vertical -- and the system can be viewed as asimple model for the Japanese kasamawashi (turning umbrella) performance art --and in that case we study the (stability of the) equilibria of the5-dimensional reduced system.

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