An invariant classification scheme of algebraically
general rotating dust with a purely electric Weyl tensor is
presented. It turns out that the vorticity vector of the dust
congruence is necessarily parallel to a Weyl principal vector, which
is moreover geodesic. An explicit metric expression can be obtained
for the subclass of expanding models with one functionally
independent zero-order Riemann invariant. The basic equations for
the general case, where there are two such invariants, are given
within a weighted 1+1+2 tetrad formalism.