  We propose an evolutionary model to describe the dynamical evolution of star
cluster systems in tidal fields, in which we calibrated the parametric
equations defining the model by running direct N-body simulations of star
clusters with a wide range of initial masses and set of orbital parameters,
living within the external tidal field generated by a disc-like galaxy. We
derived a new method to solve numerically the evolutionary equations, allowing
us to infer constraints on the mass of a star cluster from its age, present-day
mass, orbital parameters and external gravitational potential. The result has
been applied to the metal-rich subsample of Galactic globular clusters, being a
good representation of a disc-bulge population. We reconstructed the initial
mass function of these objects from the present-day mass function, finding that
a lognormal distribution is well preserved during the evolution of the globular
cluster system. The evolution of a power-law initial mass function has been
evaluated, confirming that it transforms into a lognormal distribution of the
cluster masses within an Hubble time. Our results are consistent with a
formation scenario in which metal-rich Galactic globular clusters formed from
giant molecular clouds in high-pressure regions during the early phases of the
evolution of the Galactic disc and bulge.
