Seminario

Seminario Geometría, Mecánica y Control

Ball on a Rotating Cup

Ponente:  Nicola Sansonetto (University of Verona)
Fecha:  viernes 01 de octubre de 2021 - 15:30
Lugar:  Online - us06web.zoom.us/j/7555463367 (ID: 755 546 3367)

Resumen:

In this seminar I will introduce and study the class of nonholonomic mechanical systems formed by a heavy symmetric ball that rolls without sliding on a surface of revolution, which is either at rest or rotates about its (vertical) figure axis with uniform angular velocity Ω.
I will show that the reduced system is Hamiltonizable even if Ω is not vanishing and, exploiting the recently introduced ‘moving energy’, we give sufficient conditions on the profile of the surface that ensure the periodicity of the reduced dynamics and hence the quasi-periodicity of the unreduced dynamics on tori of dimension up to three. Furthermore, we determine all the equilibria of the reduced system, which are classified in three distinct families, and determine their stability properties.

The seminar is based on the collaboration with F. Fasso` and M. Dalla Via 
"On the dynamics of a heavy symmetric ball that rolls without sliding on a uniformly rotating surface of revolution” 
Preprint https://arxiv.org/abs/2109.00236