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Mechanics of ship capsize under direct and parametric wave excitation

The equations of motion of a ship that is simultaneously heaving, swaying and rolling in waves are derived from first principles in a manner that allows considerable generalization of the sea-state, and offers a systematic approximation of the hydrodynamic pressures by an expansion of the velocity potential in circular harmonics. Assumption of static balance in heave reduces the problem to a single roll equation with both direct and parametric excitation, the latter multiplying the conventional GZ restoring function. Numerical steady-state and transient studies of an archetypal biased boat confirm that our earlier conclusions, about basin erosion and the importance of transient capsize, are preserved under realistic magnitudes of parametric excitation.