MECHANICS OF SHIP CAPSIZE UNDER DIRECT AND PARAMETRIC WAVE EXCITATION

The equations of motion of a ship that is simultaneously heaving, sway ing 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 expansi on of the velocity potential in circular harmonics. Assumption of stat ic balance in heave reduces the problem to a single roll equation with both direct and parametric excitation, the latter multiplying the con ventional GZ restoring function. Numerical steady-state and transient studies of an archetypal biased boat confirm that our earlier conclusi ons, about basin erosion and the importance of transient capsize, are preserved under realistic magnitudes of parametric excitation.