Gravitational softening as a smoothing operation
  In self-consistent N-body simulations of collisionless systems, gravitational
interactions are modified on small scales to remove singularities and simplify
the task of numerically integrating the equations of motion. This
`gravitational softening' is sometimes presented as an ad-hoc departure from
Newtonian gravity. However, softening can also be described as a smoothing
operation applied to the mass distribution; the gravitational potential and the
smoothed density obey Poisson's equation precisely. While `softening' and
`smoothing' are mathematically equivalent descriptions, the latter has some
advantages. For example, the smoothing description suggests a way to set up
N-body initial conditions in almost perfect dynamical equilibrium.
