Abstract
Abstract A new analysis of nonlinear rolling carried out by the multiscale perturbation method is herewith presented. The behaviour of a ship in a regular beam sea is considered and approximate analytical solutions in three nonlinear resonance regions are obtained. These concern the transient and the steady state roll oscillations. The latter fits in well with a previous one obtained through the averaging method and with the results of the numerical simulation. The obtained results appear to be particularly convenient due to their major mathematical simplicity. Moreover, they allow a simple estimation of the maximum roll amplitudes predictable for a given excitation intensity.
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