The sea-wave elevation and multistability in a non-autonomous nonlinear Itô’s stochastic differential equation for the rolling angle of a ship

Prediction of the rolling behavior of ships in irregular sea remains one of the most difficult problems in ship engineering. The present work facilitates solution of this problem by derivation of a model which is meaningful from the subject-specific point of view and can efficiently be analyzed with the path-integration method. The model is a single Itô’s stochastic differential equation for the rolling angle of a ship located at a fixed spatial point. The equation appears to be of the third order and nonlinear. It takes into account the elevation of stochastic traveling sea waves. The stochasticity of the elevation is allowed for by stationary stochastic velocity of the waves. The works also notes the picture for the multistability of the derived model. Improvement of capabilities of the methods for multistable nonlinear systems is included in directions for future research.