Static Equilibria of Rigid Bodies: Dice, Pebbles, and the Poincare-Hopf Theorem

@article{Vrkonyi2006StaticEO,
  title={Static Equilibria of Rigid Bodies: Dice, Pebbles, and the Poincare-Hopf Theorem},
  author={P{\'e}ter L. V{\'a}rkonyi and G{\'a}bor Domokos},
  journal={J. Nonlinear Science},
  year={2006},
  volume={16},
  pages={255-281}
}
By appealing to the Poincaré-Hopf Theorem on topological invariants, we introduce a global classification scheme for homogeneous, convex bodies based on the number and type of their equilibria. We show that beyond trivially empty classes all other classes are non-empty in the case of three-dimensional bodies; in particular we prove the existence of a body with just one stable and one unstable equilibrium. In the case of two-dimensional bodies the situation is radically different: the class with… CONTINUE READING