  We report on a study of a classical, finite system of confined particles in
two dimensions with a two-body repulsive interaction. We first develop a simple
analytical method to obtain equilibrium configurations and energies for few
particles. When the confinement is harmonic, we prove that the first transition
from a single shell occurs when the number of particles changes from five to
six. The shell structure in the case of an arbitrary number of particles is
shown to be independent of the strength of the interaction but dependent only
on its functional form. It is also independent of the magnetic field strength
when included. We further study the effect of the functional form of the
confinement potential on the shell structure. Finally we report some
interesting results when a three-body interaction is included, albeit in a
particular model.
