  Motivated by recent experiments, we theoretically study a gas of atomic
bosons confined in an elliptical harmonic trap; forming a quasi-two-dimensional
atomic Bose-Einstein condensate subject to a density-dependent gauge potential
which realises an effective density-angular-momentum coupling. We present exact
Thomas-Fermi solutions which allows us to identify the stable regimes of the
full parameter space of the model. Accompanying numerical simulations reveal
the effect of the interplay of the rigid body and density-angular-momentum
coupling for the elliptically confined condensate. By varying the strength of
the gauge potential and trap anisotropy we explore how the superfluid state
emerges in different experimentally accessible geometries, while for large
rotation strengths dense vortex lattices and concentric vortex ring
arrangements are obtained.
