  We describe an algorithm for constructing N-body realizations of equilibrium
spherical systems. A general form for the mass density rho(r) is used, making
it possible to represent most of the popular density profiles found in the
literature, including the cuspy density profiles found in high-resolution
cosmological simulations. We demonstrate explicitly that our models are in
equilibrium. In contrast, many existing N-body realizations of isolated systems
have been constructed under the assumption that the local velocity distribution
is Maxwellian. We show that a Maxwellian halo with an initial r^{-1} central
density cusp immediately develops a constant-density core. Moreover, after just
one crossing time the orbital anisotropy has changed over the entire system,
and the initially isotropic model becomes radially anisotropic. These effects
have important implications for many studies, including the survival of
substructure in cold dark matter (CDM) models. Comparing the evolution and
mass-loss rate of isotropic Maxwellian and self-consistent Navarro, Frenk, &
White (NFW) satellites orbiting inside a static host CDM potential, we find
that the former are unrealistically susceptible to tidal disruption. Thus,
recent studies of the mass-loss rate and disruption timescales of substructure
in CDM models may be compromized by using the Maxwellian approximation. We also
demonstrate that a radially anisotropic, self-consistent NFW satellite loses
mass at a rate several times higher than that of its isotropic counterpart on
the same external tidal field and orbit.
