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. 409423
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 5dimensional $\textrm{SO(3)}$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 5dimensional reduced system.
