The rolling motion of a ship has been described by a nonlinear differential equation explicitly taking into account the nonlinearities in both the restoring and the damping. A perturbative analysis in the main resonance frequency region, relative to a regular beam sea, allows to estimate the maximum amplitudes as a function of the excitation intensity. This is obtained through an algebraic equation from which the approximate solutions can be given in explicit form. To this effect, a simple formula relating the excitation to the maximum rolling is found. A comparison with experimental results shows quite a good agreement.
