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SUMMARY:Painlevé Paradox for Oblique Impact of Rigid Body with Friction -
  Yunian Shen (Nanjing University Science and Technology)
DTSTART:20100507T153000Z
DTEND:20100507T160000Z
UID:TALK24530@talks.cam.ac.uk
CONTACT:Rebecca Loving
DESCRIPTION:Using a full rigid body model\, Painlevé (1895) found that in
 consistency (no solution) or indeterminacy (non-unique solution) can occur
  in analyses of oblique impact for rigid bodies colliding against a contac
 t surface with a large coefficient of friction. This dynamic phenomenon is
  called Painlevé paradox. Mainly\, this talk focuses on explaining the ca
 use of Painlevé paradox and describing how to resolve the problem. The as
 sumptions of a rigid body model and their contribution to the Painlevé pa
 radox are explained thoroughly from 3 aspects including constraint conditi
 ons\, governing equations and physics behaviour. The Painlevé paradox can
  be resolved by considering the compliance of the contact region between t
 he colliding bodies. Based on a hybrid analytical model\, a unique solutio
 n is obtained for the case of Painlevé paradox. The dynamic properties of
  this paradox are investigated further. Theoretical analysis indicates tha
 t\, other than a case of β32=0\,  Painlevé paradox only occurs in a regi
 on of Linear Complementarity Problem (LCP) identical to the jam (self-lock
 ing) region of oblique impact. Irrespective of the initial value of tangen
 tial relative velocity\, the jam process always goes through three periods
 : sliding\, stick\, and terminal (reverse) sliding. 
LOCATION:Cambridge University Engineering Department\, Oatley Seminar Room
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