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SUMMARY:Mono-monostatic bodies: the story of the Gömböc - Gabor Domokos
DTSTART:20071116T143000Z
DTEND:20071116T153000Z
UID:TALK8272@talks.cam.ac.uk
CONTACT:Nami Norman
DESCRIPTION:ABSTRACT:\n\nThe weeble (also called the “Comeback Kid”) i
 s the favorite of many  \nchildren: whenever knocked over\, it always retu
 rns to the same  \n(stable) equilibrium position. This toy is\, of course\
 , not  \nhomogenous\, spontaneous self-righting is guaranteed by the weigh
 t at  \nthe bottom. We may also observe that most weebles have only one  \
 nunstable balance point\, at the top.\n\nWhen we look at homogeneous objec
 ts\, the problem becomes less  \ntrivial. In two dimensions\, it is relati
 vely easy to prove that  \nhomogeneous weebles do not exist. In three dime
 nsions the question  \nwas open until\, in 1995\, V.I. Arnold conjectured 
 that convex\,  \nhomogeneous solids with just one stable and one unstable 
 point of  \nequilibrium (also called mono-monostatic) may exist. These are
   \n“special weebles” which share the number and type of equilibria of
   \nthe toy\, however\, no weight is added.\n\nNot only did the celebrated
  mathematician’s conjecture turn out to be  \ntrue\, the newly discovere
 d objects show various interesting features.  \nMono-monostatic bodies are
  neither flat\, nor thin\, they are not  \nsimilar to typical objects with
  more equilibria and they are hard to  \napproximate by polyhedra. Moreove
 r\, there seems to be strong  \nindication that these forms appear in Natu
 re due to their special  \nmechanical properties. In particular\, the shel
 l of some terrestrial  \nturtles looks rather similar and systematic measu
 rements confirmed  \nthat the similarity is not a coincidence.\n\n\nRefere
 nces:\n\n1.  http://www.gomboc.eu\n2.  Domokos\, G.\, Ruina\, A.\, Papadop
 oulos\, J.: Static equilibria of  \nrigid   bodies: is there anything new?
  J. Elasticity\, 36 (1994)\, 59-66.\n3.  Varkonyi\, P. \, Domokos G.:  Sta
 tic equilibria of rigid bodies:  \ndice\, pebbles and the Poincare-Hopf Th
 eorem. J. Nonlinear Science 16  \n(2006)\, 255-281.\n4.  Varkonyi\, P.\, D
 omokos G.: Monos-monostatic bodies: the answer to  \nArnold's question. Th
 e Mathematical Intelligencer\, 28 (2006) (4) pp. \n34-36\n
LOCATION:Department of Engineering - LR6
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