Abstract
The problem of ship rolling in the stochastic wave has been studied in the past. In this paper the stochastic nonlinear dynamic behaviors including stochastic chaotic motion and probability density function of ship rolling are studied by nonlinear dynamic method and probability theory. The random Melnikov mean-square criterion is used to determine the parameter domain for ship's random chaotic motion. The probability density function of rolling response is evaluated in the chaotic parameter domain using path integral method. The time-dependent probability of ship rolling restricted within the safe domain is provided and capsizing is investigated in the probability's view.
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