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2013
Impact Factor

Nicola Sansonetto

University of Verona

Publications:

Fasso F., Sansonetto N.
On Some Aspects of the Dynamics of a Ball in a Rotating Surface of Revolution and of the Kasamawashi Art
2022, vol. 27, no. 4, pp.  409-423
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 blowup. This is done by 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.
Keywords: nonholonomic mechanical systems with symmetry, rolling rigid bodies, relative equilibria, kasamawashi
Citation: Fasso F., Sansonetto N.,  On Some Aspects of the Dynamics of a Ball in a Rotating Surface of Revolution and of the Kasamawashi Art, Regular and Chaotic Dynamics, 2022, vol. 27, no. 4, pp. 409-423
DOI:10.1134/S1560354722040025

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