  We introduce and study the mechanical system which describes the dynamics and
statics of rigid bodies of constant density floating in a calm incompressible
fluid. Since much of the standard equilibrium theory, starting with Archimedes,
allows bodies with vertices and edges, we assume the bodies to be convex and
take care not to assume more regularity than that implied by convexity. One
main result is the (Liapunoff) stability of equilibria satisfying a condition
equivalent to the standard 'metacentric' criterion.
