  Systems whose potential energies consists of pieces that scale as r^-2
together with pieces that scale as r^2, show no violent relaxation to Virial
equilibrium but may pulsate at considerable amplitude for ever. Despite this
pulsation these systems form lattices when the non-pulsational `energy' is low,
and these disintegrate as that energy is increased. The `specific heats' show
the expected halving as the `solid' is gradually replaced by the `fluid' of
independent particles. The forms of the lattices are described here for N ~ 20
and they become hexagonal close packed for large N. In the larger N limit, a
shell structure is formed. Their large N behaviour is analogous to a gamma=5/3
polytropic fluid with a quasi-gravity such that every element of fluid attracts
every other in proportion to their separation. For such a fluid, we study the
`rotating pulsating equilibria' and their relaxation back to uniform but
pulsating rotation. We also compare the rotating pulsating fluid to its
discrete counter part, and study the rate at which the rotating crystal
redistributes angular momentum and mixes as a function of extra heat content.
