  We consider the rotating and translating equilibria of open finite vortex
sheets with endpoints in two-dimensional potential flows. New results are
obtained concerning the uniqueness and stability of these equilibrium
configurations which complement analogous results known for unbounded, periodic
and circular vortex sheets. First, we demonstrate that, within the class of
rotating configurations involving a single open vortex sheet with endpoints,
the straight segment revolving around its midpoint is a unique equilibrium.
Second, we show that the rotating and translating equilibria of finite vortex
sheets are linearly unstable. However, while in the first case unstable
perturbations grow exponentially fast in time, the growth of such perturbations
in the second case is algebraic. In both cases the growth rates are increasing
functions of the wavenumbers of the perturbations. Remarkably, these stability
results are obtained entirely with analytical computations. Third, we obtain
and analyze equations describing the time evolution of a straight vortex sheet
in linear external fields. Finally, it is demonstrated that the results
concerning the linear stability analysis of the rotating sheet are consistent
with the infinite-aspect limit of the stability results known for Kirchhoff's
ellipse (Love 1893; Mitchell & Rossi 2008) and that the solutions we obtained
accounting for the presence of external fields are also consistent with the
infinite-aspect limits of the analogous solutions known for vortex patches.
