  We present results from a series of high-resolution N-body simulations that
focus on the formation and evolution of eight dark matter halos, each of order
a million particles within the virial radius. We follow the time evolution of
hundreds of satellite galaxies with unprecedented time resolution, relating
their physical properties to the differing halo environmental conditions. The
self-consistent cosmological framework in which our analysis was undertaken
allows us to explore satellite disruption within live host potentials, a
natural complement to earlier work conducted within static potentials. Our host
halos were chosen to sample a variety of formation histories, ages, and
triaxialities; despite their obvious differences, we find striking similarities
within the associated substructure populations. Namely, all satellite orbits
follow nearly the same eccentricity distribution with a correlation between
eccentricity and pericentre. We also find that the destruction rate of the
substructure population is nearly independent of the mass, age, and triaxiality
of the host halo. There are, however, subtle differences in the velocity
anisotropy of the satellite distribution. We find that the local velocity bias
at all radii is greater than unity for all halos and this increases as we move
closer to the halo centre, where it varies from 1.1 to 1.4. For the global
velocity bias we find a small but slightly positive bias, although when we
restrict the global velocity bias calculation to satellites that have had at
least one orbit, the bias is essentially removed.
