  We have developed a simple yet surprisingly accurate analytic scheme for
tracking the dynamical evolution of substructure within larger dark halos. The
scheme incorporates the effects of dynamical friction, tidal mass loss and
tidal heating via physically motivated approximations. Using our scheme, we can
predict the orbital evolution and mass-loss history of individual subhalos in
detail. We are also able to determine the impact and importance of the
different physical processes on the dynamical evolution of the subhalos. To
test and calibrate this model, we compare it with a set of recent
high-resolution numerical simulations of mergers between galaxies and small
companions. We find that we can reproduce the orbits and mass-loss rates seen
in all of these simulations with considerable accuracy, using a single set of
values for the three free parameters in our model. Computationally, our scheme
is more than 1000 times faster than the simplest of the high-resolution
numerical simulations. This means that we can carry out detailed and
statistically meaningful investigations into the characteristics of the subhalo
population in different cosmologies, the stripping and disruption of the
subhalos, and the interactions of the subhalos with other dynamical structures
such as a thin disk. This last point is of particular interest given the
ubiquity of minor mergers in hierarchical models. In this regard, our method's
simplicity and speed makes it particularly attractive for incorporation into
semi-analytic models of galaxy formation.
