  The unsteady electrorotation of a drop of a viscous weakly conducting
polarizable liquid suspended in another viscous weakly conducting polarizable
liquid immiscible with the former in an applied constant uniform electric field
is theoretically investigated. The surface tension of the drop is regarded as
sufficiently large for deformation of the drop under the action of the applied
electric field and the electrohydrodynamic flow can be considered small and the
drop can be considered spherical in the calculation of the electric field and
flow. The electric field intensity and the velocity and pressure in the
electrohydrodynamic flow are sought for in the form of a series solution with
time-dependent scalar, vector, and tensor coefficients for which relations are
found allowing one to determine them. The coefficients are sought for in the
form of asymptotic expansions over the parameter, the smallness of which
corresponds to the sufficiently large viscosity of the drop with respect to
that of the surrounding liquid. The differential equations for the terms of the
dimensionless expansions up to the first and second orders with respect to this
parameter are obtained. Their stationary solutions are found in the explicit
form and their stability is investigated. Up to the terms of the second order,
transitions to deformational oscillations of the drop are established not to
occur.
