Stochastic rolling motion of ships in following seas

The aim of this study is to examine both the stochastic rolling motion of ships in following seas by using analytical and numerical safe basin concept and to show how the concept of safe basin can be utilized for the assessment of the stability of ships. First, the boundary of the analytic safe basins of stochastic rolling motion is obtained by using the Lyapunov function used by Schurz (2009). Second, the safe basins of stochastic rolling motion are obtained numerically by using stochastic Euler (Euler–Maruyama) method. It is concluded that the analytically and numerically obtained safe basins are coherent. Lastly, the practical intact stability criterion for ships in following seaway is developed by proposing a formula given for the maximum width of analytic safe basin.