NONLINEAR ROLLING MOTIONS OF SHIPS IN LONGITUDINAL WAVES

An analytical-numerical technique is used to predict the qualitative changes taking place as one of the parameters is slowly changed. Analog- and digital-computer simulations confirm the accuracy of the predictions and complement the qualitative peculiarities of the dynamics. The results of the analysis and computer simulations are summarized in a bifurcation diagram that displays the instability boundaries. It is found that very dangerous resonant regions cannot be predicted by using the linearized equation. Capsizing is found to occur via two distinct scenarios: one evolving from a large oscillation through a disappearance of a chaotic attractor (crises), and a second, potentially more dangerous, developing from a small oscillation through a sudden tangent instability