Скачать или смотреть GFSW04 | Prof. Keith Moffatt | The beaver ball: a chaotic rolling robot

GFSW04 | Prof. Keith Moffatt | The beaver ball: a chaotic rolling robot

Speaker: Professor Keith Moffatt (University of Cambridge)
Date: 30th Nov 2017 - 9:30 to 10:10
Venue: INI Seminar Room 1
Title: The beaver ball: a chaotic rolling robot
Event: (GFSW04) Form in art, toys and games
Abstract: Equations describing the rolling of a spherical ball on a
horizontal surface are obtained, the motion being activated by an internal
rotor driven by a battery mechanism. The rotor is modelled as a point mass
mounted inside a spherical shell, and caused to move in a prescribed circular
orbit relative to the shell. The system is described in terms of four
independent dimensionless parameters. The equations governing the angular momentum
of the ball relative to the point of contact with the plane constitute a
six-dimensional, non-holonomic, non-autonomous dynamical system with cubic
nonlinearity. This system is decoupled from a subsidiary system that describes
the trajectories of the center of the ball. Numerical integration of these
equations for prescribed values of the parameters and initial conditions
reveals a tendency towards chaotic behaviour as the radius of the circular
orbit of the point mass increases (other parameters being held constant). It is
further shown that there is a range of values of the initial angular velocity
of the shell for which chaotic trajectories are realised while contact between
the shell and the plane is maintained.

The predicted behaviour has been observed in our
experiments.



Work in collaboration with V.A.Vladimirov and K. Ilin

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