Bodies floating in still water are subject to the laws of rigid body mechanics combined with Archimedes' principle. We write down the equations governing their dynamics. These equations take the form of a Hamiltonian system similar to, but richer in structure than, the well-known heavy top. The sometimes surprising equilibrium configurations of floating bodies have attracted interest from the times of Archimedes up until today. The stability properties of equilibria have essentially been known since the 18th century and extensively used in naval architecture and by glaciologists studying icebergs. We give a precise statement of these stability criteria and an elementary proof of nonlinear stability under time evolution.
