We report the first successful molecular dynamics simulations of fullerene annealing and fragmentation. The molecular vibrational dynamics, which we find to play a central role in these processes, is simulated by following constant energy trajectories under specially generated initial conditions. Employing this scheme with a carbon tight-binding potential, we have observed sequential ${\mathrm{C}}_{2}$ loss from ${\mathrm{C}}_{60}$, as well as the rearrangement of carbon-carbon bonds on the fullerene cage. Our successful approach is a departure from previously employed constant temperature schemes.