A fully analytical method to assess the risk of capsizing in beam sea

The capsizing issue needs new approaches. An analytical calculation of the capsize probability could lead to a faster computation of the probability for any ship. Markov methods have proved to have a good approach to evaluate the probability density function of the variables involved in the roll motion. Therefore, an analytical calculation of the probability density function of the variables involved in the roll motion has been conducted following a Markov method. The results given by this calculation are supposed to be first considered in a theoretical point of view. The assumptions made to conduct the calculations are as follows: the roll motion dynamics can be represented with a 1-degree-of-freedom model; the damping is linear; the restoring moment is non-linear and 2 π -periodic. The capsize probability could be calculated if the characteristics of the roll motion when a ship is capsizing is known. In this way, a study about capsize criterion in beam sea is added to describe the characteristics of the capsizing ship’s roll motion.