May 14, 2010, 1100 Webb

In the first part of this talk, I introduce an intriguing problem of rigid body mechanics proposed by V.I. Arnold: is there a convex, homogeneous object, which has less than four orientations corresponding to static equilibria on a horizontal plane? I show why most bodies have at least four equilibria, and construct a special example called ‘Gomboc’ with only two. I also demonstrate that such objects are very sensitive to small perturbations, and are unlikely to be found accidentally. The second part of the talk is devoted to applications. Most importantly, we will count equilibria of turtle shells, and I will talk about the relevance of this number to the evolution of shell morphology and the self-righting strategies of the animals.

Peter Varkonyi has been assistant professor at the Budapest University of Technology since 2006. He received his MSc (2003), and his PhD (2006) in Architectural Engineering from the same institution. He is currently visitor at Caltech, Mechanical Engineering, and in 2006-07 he was visitor at the Program in Applied and Computational Mathematics at Princeton University. In 2008, he was awarded the Knight’s Cross Order of Merit of the Republic of Hungary as coinventor of the ‘Gomboc’- which is a subject of the seminar talk. His research interests include structural optimization, rigid body dynamics, abrasive processes, and the dynamics of oscillator networks.