 
Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Spring 2010 Seminar Series
Presents
Static Equilibria of Rigid Bodies: from Monostatic Shapes
to Optimal Turtles
Peter Varkonyi
Budapest University of Technology
Friday, May 14, 2010, 3:00 4:00pm WEBB 1100
Abstract:
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, homogenous 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 con
struct 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 selfrighting strategies of the
animals.
About the Speaker:
Peter Varkonyi has been assistant professor at the Budapest University of Technology since 2006. He
