  The Galilean satellites' dynamics has been studied extensively during the
last century. In the past it was common to use analytical expansions in order
to get simple models to integrate, but with the new generation computers it
became prevalent the numerical integration of very sophisticated and almost
complete equations of motion. In this article we aim to describe the resonant
and secular motion of the Galilean satellites through a Hamiltonian, depending
on the slow angles only, obtained with an analytical expansion of the
perturbing functions and an averaging operation. In order to have a model as
near as possible to the actual dynamics, we added perturbations and we
considered terms that in similar studies of the past were neglected, such as
the terms involving the inclinations and the Sun's perturbation. Moreover, we
added the tidal dissipation into the equations, in order to investigate how
well the model captures the evolution of the system.
