  The applicability of the highly idealized secondary infall model to
`realistic' initial conditions is investigated. The collapse of proto-halos
seeded by $3\sigma$ density perturbations to an Einstein--de Sitter universe is
studied here for a variety of scale-free power spectra with spectral indices
ranging from $n=1$ to $-2$. Initial conditions are set by the constrained
realization algorithm and the dynamical evolution is calculated both
analytically and numerically. The analytic calculation is based on the simple
secondary infall model where spherical symmetry is assumed. A full numerical
simulation is performed by a Tree N-body code where no symmetry is assumed. A
hybrid calculation has been performed by using a monopole term code, where no
symmetry is imposed on the particles but the force is approximated by the
monopole term only. The main purpose of using such code is to suppress
off-center mergers. In all cases studied here the rotation curves calculated by
the two numerical codes are in agreement over most of the mass of the halos,
excluding the very inner region, and these are compared with the analytically
calculated ones. The main result obtained here, reinforces the foundings of
many N-body experements, is that the collapse proceeds 'gently' and not {\it
via} violent relaxation. There is a strong correlation of the final energy of
individual particles with the initial one. In particular we find a preservation
of the ranking of particles according to their binding energy. In cases where
the analytic model predicts non-increasing rotation curves its predictions are
confirmed by the simulations. Otherwise, sensitive dependence on initial
conditions is found and the analytic model fails completely.
