  Motivated by recent experimental and theoretical studies of fewparticle
vortex clusters in Bose-Einstein condensates, we consider the ordinary
differential equations of motion and systematically examine settings for up to
N = 6 vortices. We analyze the existence of corresponding stationary state
configurations and also consider their spectral stability properties. We
compare our particle model results with the predictions of the full partial
differential equation system. Whenever possible, we propose generalizations of
these results in the context of clusters of N vortices. Some of these, we can
theoretically establish, especially so for the N-vortex polygons, while others
we state as conjectures, e.g. for the N-vortex line equilibrium.
