MELNIKOV ANALYSIS FOR A SHIP WITH A GENERAL ROLL-DAMPING MODEL

In the framework of a general roll-damping model, we study the influen ce of different damping models on the nonlinear roll dynamics of ships through a detailed Melnikov analysis. We introduce the concept of the Melnikov equivalent damping and use phase-plane concepts to obtain si mple expressions for what we call the Melnikov damping coefficients. W e also study the sensitivity of these coefficients to parameter variat ions. As an application, we consider the equivalence of the linear-plu s-cubic and linear-plus-quadratic damping models, and we derive a cond ition under which the two models yields the same Melnikov predictions. The free- and forced-oscillation behaviors of the models satisfying t his condition are also compared.