Ship Capsizing in Random Sea Waves and the Mathentical Pendulum
The ship capsizing is treated as a first-passage problem by using the method of asymptotic expansion solutions of the Pontryagin’s differential equation . The analysis includes first- and second-order asymptotic approximations for the mean exit time based on perturbation analysis of diffusion processes [2–4]. Related work of first-passage problem has been considered by others [5–9]. The ship governing equation of motion is related to a great extent to the motion of the mathematical pendulum in the rotational motion regime. In this case the analysis is extended to include an approximate solution of the Fokker-Planck equation for stationary probability density. Conditions for stochastic bifurcation in probability are obtained.
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