  We develop a generic method to compute the dynamics induced by quenches in
completely connected quantum systems. These models are expected to provide a
mean-field description at least of the short time dynamics of finite
dimensional system. We apply our method to the Bose-Hubbard model, to a
generalized Jaynes-Cummings model, and to the Ising model in a transverse
field. We find that the quantum evolution can be mapped onto a classical
effective dynamics, which involves only a few intensive observables. For some
special parameters of the quench, peculiar dynamical transitions occur. They
result from singularities of the classical effective dynamics and are
reminiscent of the transition recently found in the fermionic Hubbard model.
Finally, we discuss the generality of our results and possible extensions.
