Abstract
A new mathematical model with nonlinearities defined up to the third order in terms of the heave, roll and pitch couplings is introduced, in order to simulate strong roll parametric amplifications in head seas. The influence of hull stern shape is discussed. A theoretical analysis discloses some essential dynamical characteristics associated with the proposed coupled third order mathematical model The influence of nonlinear terms on the dynamics of roll parametric resonance appears to be relevant for low metacentric conditions and extreme waves in the head seas condition.
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