Catastrophe Analysis on Ship Single-degree-of-freedom Nonlinear Rolling

While establishing the ship´s single-degree-of-freedom nonlinear rolling equation, damping moment and restoring moment were approximated to cube and seven times separately for convenience. On the basis of this, catastrophe theory was applied to analyze the ship capsize problem caused by single-degree-of-freedom nonlinear rolling in regular waves. Through mathematical manipulation, the ship´s nonlinear rolling model was transformed into cusp catastrophe model, and the catastrophe phenomenon was analyzed. The results showed that the ship´s natural rolling frequency and the restoring force coefficient were related in the occurrence of capsize. By mathematical derivation, the relational expression between natural rolling frequency and the restoring force coefficient was deduced, and the relationship curve between them was mapped, which had some practical significance for ship parameters designing to prevent capsizing.