  The main goal of this paper is to set up a numerical laboratory for the study
of the slow evolution of the density and of the pressure tensor profiles of an
otherwise collisionless stellar system, as a result of the interactions with a
minority component of heavier "particles".The effects that we would like to
study are those attributed to slow collisional relaxation and generically
called "dynamical friction". We start by revisiting the problem of the sinking
of a satellite inside an initially isotropic, non-rotating, spherical galaxy,
which we follow by means of N-body simulations using about one million
particles. We then consider a quasi-spherical problem, in which the satellite
is fragmented into a set of many smaller masses with a spherically symmetric
initial density distribution. In a wide set of experiments, designed in order
to bring out effects genuinely associated with dynamical friction, we are able
to demonstrate the slow evolution of the density profile and the development of
a tangentially biased pressure in the underlying stellar system, while we
briefly address the issue of the circularization of orbits induced by dynamical
friction on the population of fragments. The results of the simulations
presented here and others planned for future investigations allow us to study
the basic mechanisms of slow relaxation in stellar systems and thus may be of
general interest for a variety of problems, especially in the cosmological
context. Here our experiments are conceived with the specific goal to clarify
some mechanisms that may play a role in the evolution of an elliptical galaxy
as a result of the interaction between the stars and a significant population
of globular clusters or of the merging of a large number of small satellites.
