  We investigate numerically the response of an atomic Bose-Einstein condensate
to a weakly-elliptical rotating trap over a large range of rotation
frequencies. We analyse the quadrupolar shape oscillation excited by rotation,
and discriminate between its stable and unstable regimes. In the latter case,
where a vortex lattice forms, we compare with experimental observations and
find good agreement. By examining the role of thermal atoms in the process, we
infer that the process is temperature-independent, and show how terminating the
rotation gives control over the number of vortices in the lattice. We also
study the case of critical rotation at the trap frequency, and observe large
centre-of-mass oscillations of the condensate.
