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CATEGORIES:Engineering Department Mechanics Colloquia Researc
h Seminars
SUMMARY:Mono-monostatic bodies: the story of the Gömböc -
Gabor Domokos
DTSTART;TZID=Europe/London:20071116T143000
DTEND;TZID=Europe/London:20071116T153000
UID:TALK8272AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/8272
DESCRIPTION:ABSTRACT:\n\nThe weeble (also called the “Comeback
Kid”) is the favorite of many \nchildren: whenev
er knocked over\, it always returns to the same \
n(stable) equilibrium position. This toy is\, of c
ourse\, not \nhomogenous\, spontaneous self-right
ing is guaranteed by the weight at \nthe bottom.
We may also observe that most weebles have only on
e \nunstable balance point\, at the top.\n\nWhen
we look at homogeneous objects\, the problem becom
es less \ntrivial. In two dimensions\, it is rela
tively easy to prove that \nhomogeneous weebles d
o not exist. In three dimensions the question \nw
as open until\, in 1995\, V.I. Arnold conjectured
that convex\, \nhomogeneous solids with just one
stable and one unstable point of \nequilibrium (a
lso called mono-monostatic) may exist. These are
\n“special weebles” which share the number and typ
e of equilibria of \nthe toy\, however\, no weigh
t is added.\n\nNot only did the celebrated mathema
tician’s conjecture turn out to be \ntrue\, the n
ewly discovered objects show various interesting f
eatures. \nMono-monostatic bodies are neither fla
t\, nor thin\, they are not \nsimilar to typical
objects with more equilibria and they are hard to
\napproximate by polyhedra. Moreover\, there seem
s to be strong \nindication that these forms appe
ar in Nature due to their special \nmechanical pr
operties. In particular\, the shell of some terres
trial \nturtles looks rather similar and systemat
ic measurements confirmed \nthat the similarity i
s not a coincidence.\n\n\nReferences:\n\n1. http:
//www.gomboc.eu\n2. Domokos\, G.\, Ruina\, A.\, P
apadopoulos\, J.: Static equilibria of \nrigid
bodies: is there anything new? J. Elasticity\, 36
(1994)\, 59-66.\n3. Varkonyi\, P. \, Domokos G.:
Static equilibria of rigid bodies: \ndice\, pebb
les and the Poincare-Hopf Theorem. J. Nonlinear Sc
ience 16 \n(2006)\, 255-281.\n4. Varkonyi\, P.\,
Domokos G.: Monos-monostatic bodies: the answer t
o \nArnold's question. The Mathematical Intellige
ncer\, 28 (2006) (4) pp. \n34-36\n
LOCATION:Department of Engineering - LR6
CONTACT:Nami Norman
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