COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Engineering Department - Mechanics Colloquia Research Seminars > Mono-monostatic bodies: the story of the Gömböc

## Mono-monostatic bodies: the story of the GömböcAdd to your list(s) Download to your calendar using vCal - Gabor Domokos
- Friday 16 November 2007, 14:30-15:30
- Department of Engineering - LR6.
If you have a question about this talk, please contact Nami Norman. ABSTRACT : The weeble (also called the “Comeback Kid”) is the favorite of many children: whenever knocked over, it always returns to the same (stable) equilibrium position. This toy is, of course, not homogenous, spontaneous self-righting is guaranteed by the weight at the bottom. We may also observe that most weebles have only one unstable balance point, at the top. When we look at homogeneous objects, the problem becomes less trivial. In two dimensions, it is relatively easy to prove that homogeneous weebles do not exist. In three dimensions the question was open until, in 1995, V.I. Arnold conjectured that convex, homogeneous solids with just one stable and one unstable point of equilibrium (also called mono-monostatic) may exist. These are “special weebles” which share the number and type of equilibria of the toy, however, no weight is added. Not only did the celebrated mathematician’s conjecture turn out to be true, the newly discovered objects show various interesting features. Mono-monostatic bodies are neither flat, nor thin, they are not similar to typical objects with more equilibria and they are hard to approximate by polyhedra. Moreover, there seems to be strong indication that these forms appear in Nature due to their special mechanical properties. In particular, the shell of some terrestrial turtles looks rather similar and systematic measurements confirmed that the similarity is not a coincidence. References: 1. http://www.gomboc.eu 2. Domokos, G., Ruina, A., Papadopoulos, J.: Static equilibria of rigid bodies: is there anything new? J. Elasticity, 36 (1994), 59-66. 3. Varkonyi, P. , Domokos G.: Static equilibria of rigid bodies: dice, pebbles and the Poincare-Hopf Theorem. J. Nonlinear Science 16 (2006), 255-281. 4. Varkonyi, P., Domokos G.: Monos-monostatic bodies: the answer to Arnold’s question. The Mathematical Intelligencer, 28 (2006) (4) pp. 34-36 This talk is part of the Engineering Department - Mechanics Colloquia Research Seminars series. ## This talk is included in these lists:- All Talks (aka the CURE list)
- Cambridge University Engineering Department Talks
- Cambridge talks
- Centre for Smart Infrastructure & Construction
- Civil Engineering Talks
- Department of Engineering - LR6
- Engineering - Division C talks
- Engineering Department - Mechanics Colloquia Research Seminars
- Engineering Department Bio- and Micromechanics Seminars
- Engineering Department Dynamics and Vibration Tea Time Talks
- Featured lists
- Interested Talks
- Lennard-Jones Centre external
- School of Technology
- Trust & Technology Initiative - interesting events
- bld31
Note that ex-directory lists are not shown. |
## Other listsExistential Risk Seminar Series facisnating Talks Queens' College Politics Society## Other talksFumarate hydratase and renal cancer: oncometabolites and beyond Sustainability 101: how to frame it, change it and steer it Measuring interacting electrons in low dimensional systems: spin-charge separation and 'replicas & tbd Renationalisation of the Railways. A CU Railway Club Public Debate. Panel comparisons: Challenor, Ginsbourger, Nobile, Teckentrup and Beck 'Honouring Giulio Regeni: a plea for research in risky environments' Fields of definition of Fukaya categories of Calabi-Yau hypersurfaces Graded linearisations for linear algebraic group actions Atiyah Floer conjecture THE MATHEMATICAL MAGIC OF MIXED REALITY |