  A general theory of homeoidally striated density profiles where no divergence
occurs, is adapted to cuspy density profiles, with a suitable choice of the
scaling density and the scaling radius. A general formulation of some physical
parameters, such as angular-momentum vector, rotational-energy tensor (both
calculated in connection with a special class of rotational velocity fields),
inertia tensor, and self potential-energy tensor, is performed. Other
potential-energy tensors involving two density profiles where the boundaries
are similar and similarly placed, are also expressed. Explicit results are
attained for three special cases of physical interest which fit to a good
extent the results of high-resolution simulations for dark matter haloes, and a
class of density profiles, which closely approximate the de Vaucouleurs
$r^{1/4}$ law for elliptical galaxies. The virial theorem in tensor form for
two-component systems is written for each subsystem, and applied to giant
elliptical galaxies. The predicted velocity dispersion along the line of sight,
in the limiting case where a principal axis points towards the observer, is
found to be consistent with observations except for (intrinsic) $E7$
configurations where the major axis points towards the observer. If dark matter
haloes host an amount of undetected baryons about twice as massive as the
stellar subsystem, and undetected baryons trace non baryonic matter therein,
two main consequences arise, namely (i) velocity dispersions along the line of
sight are lower than in absence of undetected baryons, and (ii) dark matter
haloes are dynamically ``hotter'' than stellar ellipsoids, the transition
occurring when the amount of undetected baryons is about one and a half times
that of the stellar subsystem.

Astrophysics