  We present a theoretical analysis of dilute gas Bose-Einstein condensates
with dipolar atomic interactions under rotation in elliptical traps. Working in
the Thomas-Fermi limit, we employ the classical hydrodynamic equations to first
derive the rotating condensate solutions and then consider their response to
perturbations. We thereby map out the regimes of stability and instability for
rotating dipolar Bose-Einstein condensates and in the latter case, discuss the
possibility of vortex lattice formation. We employ our results to propose
several novel routes to induce vortex lattice formation in a dipolar
condensate.
