Solving the problem of nonlinear ship roll motion using stochastic dynamics

Abstract

Due to nonlinear viscous damping and the softening characteristic of the stiffness, the roll motion of a ship exhibits complex dynamics. Specifically predicting the probabilistic characteristics of roll response in an irregular seaway is still a challenging problem and continues to be of interest for both practitioners and researchers. In this work two techniques from the theory of stochastic dynamics are applied to study the probabilistic nature of roll motion in irregular seas. The first method is the “Moment Equation method” where the roll response moment equation is formulated from a six dimensional state space rolling model with a fourth order linear filter using the Itô differential rule. The resulting moment equations are solved using a cumulant neglect technique. Alternatively in the second approach, the probability density function of the rolling response is evaluated by solving the corresponding Fokker Planck Equation of the system using “Path Integral method”.