Recent developments in dynamical systems analysis are applied and extended to the study of highly nonlinear ship rolling motion and capsizing in random beam seas. Damping and wave excitation moments are dealt with as perturbations since they are relatively small compared with inertial effects and hydrostatic righting moments. There is no restriction on the restoring moment due to hydrostatic loads, and bias effects are included. Safe and unsafe areas are defined in the phase plane of the unperturbed system model to distinguish the qualitatively different ship motions of capsize and noncapsize. Capsize events are represented by solutions passing out of the safe region. The probability of such an occurrence is studied using the Melnikov function and the concept of phaseflux rates. Expressions for the phase space flux rate are derived and evaluated by numerical integration. The correlation of phase space flux and capsize is investigated through extensive simulation. It is shown that these analytical tools provide reliable, predictive information regarding the likelihood of a vessel capsize in a given sea state.
Highly Nonlinear Rolling Motion of Biased Ships in Random Beam Seas
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Jiang, Changben, Troesch, Armin W., and Steven W. Shaw. "Highly Nonlinear Rolling Motion of Biased Ships in Random Beam Seas." J Ship Res 40 (1996): 125–135. doi: https://doi.org/10.5957/jsr.19188.8.131.52
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