The equations of motion of an ideal incompressible liquid drop trapped betw
een two parallel plates under the influence of surface tension and adhesion
forces are studied. A main result of this paper is the proof that the equa
tions of motion can be written in Hamiltonian form
F(over dot) = {F,H} for all F is an element of D.
Here D denotes a class of real-valued functions on the phase space N of the
system and the Hamiltonian H is an element of D is the energy function of
the system. This allows the derivation of an equation for the (dynamic) con
tact angle, in which the free fluid surface meets the plates. The behaviour
of the dynamic contact angle is a point of great controversy in the capill
arity literature and the derivation confirms one of the existing models. In
the second part of the paper, which can be read independently, existence a
nd stability questions for rigidly rotating drops are dealt with. The exist
ence of solutions to the equations of motion that describe rotationally sym
metric drops which rotate rigidly between the plates with constant angular
velocity is proved. These solutions can be regarded as relative equilibria
of a mechanical system with symmetry. Using ideas of the energy-momentum me
thod of Lewis, Marsden and Simo, a stability criterion for this kind of mot
ion is provided. To derive this criterion, the second derivative of the sc-
called augmented energy functional at the relative equilibrium in direction
s which are transversal to the group orbit of this equilibrium is studied.
The stability criterion is applied to rigidly rotating drops of cylindrical
shape. These represent solutions to the equations of motion in the case th
at no adhesion forces act along the plates. The result extends previous wor
k of Vogel and Lewis.