Abstract
A moment method for analysing the stochastic stability of the roll motion of a ship in an irregular seaway is examined when the restoring moment in the differential equation describing the roll motion is random time dependent in form. It is shown that when the restoring moment is characterized by a white noise process, the roll motion equation can be described by an Ito stochastic differential equation. For the Ito equation, a set of moment equations are derived whose stability is then studied by well developed stability theorems of the deterministic system. The mean square stability is considered and criteria for stability are obtained in terms of damping, roll natural frequency and a stochastic parameter.
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