Three-dimensional large-amplitude oscillations of a mercury drop were obtained by
electrical excitation in low gravity using a drop tower. Multi-lobed (from three to
six lobes) and polyhedral (including tetrahedral, hexahedral, octahedral and
dodecahedral) oscillations were obtained as well as axisymmetric oscillation patterns. The
relationship between the oscillation patterns and their frequencies was obtained, and
it was found that polyhedral oscillations are due to the nonlinear interaction of waves.
A mathematical model of three-dimensional forced oscillations of a liquid drop is
proposed and compared with experimental results. The equations of drop motion are
derived by applying the variation principle to the Lagrangian of the drop motion,
assuming moderate deformation. The model takes the form of a nonlinear Mathieu
equation, which expresses the relationships between deformation amplitude and the
driving force's magnitude and frequency.