Stability and Catastrophe Analysis for a Coupled Pitch-Roll Ship

By using nonlinear dynamic theory and catastrophe theory, a two-degree-of-freedom ship nonlinear motion was discussed. The multiple scale perturbation technique was adopted to obtain the solutions of differential equations. The stability of solution was analyzed. The bifurcation response equation and bifurcation point set at steady solutions were found. The numerical analysis result shows that the cusp catastrophe exists in bifurcation set surface. The force-response curve presents that the ship rolling amplitude would bring embranchment catastrophe in some excitation force moment conditions. This kind of embranchment catastrophe phenomenon would even lead to ship capsizing.