  This is the first of a series of articles showing how 4 dimensionally
covariant analytical procedures developed in the context of General Relativity
can be usefully adapted for application in a purely Newtonian framework where
they provide physical insights (e.g. concerning helicity currents) that are not
so easy to obtain by the traditional approach based on a 3+1 space time
decomposition. After an introductory presentation of the relevant Milne
spacetime structure and the associated Cartan connection, the essential
principles are illustrated by application to the variational formulation of
simple barotropic perfect fluid models. This variational treatment is then
extended to conservative multiconstituent self gravitating fluid models of the
more general kind that is needed for treating the effects of superfluidity in
neutron stars.
