Stability and bifurcation of a rotating liquid drop

Lewis, D., J. E. Marsden and T. S. Ratiu

J.Math. Phys., 28, 2508-2515

Abstract:

The stability and symmetry breaking bifurcation of a planar liquid drop is studied using the energy-Casimir method and singularity theory. It is shown that a rigidly rotating circular drop of radius r with surface tension coefficient $\tau$ and angular velocity ${\frac{\Omega}{2}}$ is stable if ${\frac{\Omega}{2}}$² < 3${\frac{\tau}{r^3}}$. A new brance of stable rididly rotating equilibria invariant under rotation through $\pi$ and reflection across two axes bifurcates from the branch of circular solutions when (${\frac{\Omega}{2}}$)² = 3${\frac{\tau}{r^3}}$