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SUMMARY:The beaver ball: a chaotic rolling robot - Keith Moffatt (Universi
 ty of Cambridge)
DTSTART:20171130T093000Z
DTEND:20171130T101000Z
UID:TALK96148@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Equations describing the rolling of a spherical ball on a hori
 zontal surface are obtained\, the motion being activated by an internal ro
 tor driven by a battery mechanism. The rotor is modelled as a point mass m
 ounted inside a spherical shell\, and caused to move in a prescribed circu
 lar 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 const
 itute 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 inte
 gration of these equations for prescribed values of the parameters and ini
 tial 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 th
 e initial angular velocity of the shell for which chaotic trajectories are
  realised while contact between the shell and the plane is maintained.   T
 he predicted behaviour has been observed in our experiments.  &nbsp\;  <br
 ><span><br>Work in collaboration with V.A.Vladimirov and K. Ilin</span>
LOCATION:Seminar Room 1\, Newton Institute
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