On the Probability of Large Amplitude Rolling and Capsizing as a Consequence of Bifurcations

The loss of a ship is often a consequence of large amplitude rolling. This is thus examined from a probabilistic point of view. The nonlinear rolling in a stochastic sea is analysed by means of an approximate perturbation method. The results indicate that the possibility of bifurcations to resonant or subharmonic large amplitude rolling is possible in narrow band sea. A numerical time domain simulation confirms these results and gives an indication of the probability densities of states, that in the sinusoidal limit should recover the domains of attraction.