Why simulate interacting galaxies? First, simulations can test theoretical ideas. Second, detailed simulations may help in gaining insight into real systems. Third, simulations may constrain galaxy parameters such as dark halo masses.
Simulation is not a straightforward business. A dynamical model specifies the distribution function f(r, v), which depends on six variables. Observations, at best, yield f (X, Y, VZ), a function of just three variables: two coordinates on the plane of the sky, and a line of sight velocity. Thus simulations are underdetermined; further constraints are needed to make progress. In cosmology, one may stipulate that the observed structures grew from a linear density field (r) / which depends on three coordinates; this is how the ``least action'' method (Peebles 1994) can yield well-determined results. But in studying interacting galaxies we want to understand the stellar distribution, and the stars did not evolve from linear initial conditions!
So in simulating interacting galaxies, the practice has been to build equilibrium models and drop them towards each other. This approach seems to work provided that the galaxy models and their trajectories are cosmologically plausible. One example is NGC 7252, which Hibbard & Mihos (1995) simulated successfully as the result of a direct parabolic encounter of two disk galaxies; an earlier attempt to reproduce this system with a retrograde encounter (Borne & Richstone 1991) required the galaxies to start on implausibly tight circular orbits and proved inconsistent with subsequent HI observations.