  A theory of collisionless fluids is developed in a unified picture, where
nonrotating figures with anisotropic random velocity component distributions
and rotating figures with isotropic random velocity component distributions,
make adjoints configurations to the same system. R fluids are defined and mean
and rms angular velocities and mean and rms tangential velocity components are
expressed, by weighting on the moment of inertia and the mass, respectively.
The definition of figure rotation is extended to R fluids. The generalized
tensor virial equations are formulated for R fluids and further attention is
devoted to axisymmetric configurations where, for selected coordinate axes, a
variation in figure rotation has to be counterbalanced by a variation in
anisotropy excess and vice versa. A microscopical analysis of systematic and
random motions is performed under a few general hypotheses, by reversing the
sign of tangential or axial velocity components of an assigned fraction of
particles, leaving the distribution function and other parameters unchanged
(Meza 2002). The application of the reversion process to tangential velocity
components, implies the conversion of random motion rotation kinetic energy
into systematic motion rotation kinetic energy. The application of the
reversion process to axial velocity components, implies the conversion of
random motion translation kinetic energy into systematic motion translation
kinetic energy, and the loss related to a change of reference frame is
expressed in terms of systematic (imaginary) motion rotation kinetic energy. A
procedure is sketched for deriving the spin parameter distribution (including
imaginary rotation) from a sample of observed or simulated large-scale
collisionless fluids i.e. galaxies and galaxy clusters.

Astrophysics