Ship Capsizing in Random Sea Waves and the Mathentical Pendulum

  • N. K. Moshchuk
  • R. A. Ibrahim
  • R. Z. Khasminskii
  • P. L. Chow
Part of the Solid Mechanics and its Applications book series (SMIA, volume 47)


The ship capsizing is treated as a first-passage problem by using the method of asymptotic expansion solutions of the Pontryagin’s differential equation [1]. 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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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • N. K. Moshchuk
    • 1
  • R. A. Ibrahim
    • 1
  • R. Z. Khasminskii
    • 2
  • P. L. Chow
    • 2
  1. 1.Department of Mechanical EngineeringWayne State UniversityDetroitUSA
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA

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