The theoretical background and mathematical formulations representing ship dynamics in large and steep waves are presented. The equations of ship motions in oblique waves in- clude the hydrodynamic forces imposed on the hull at large heel angles by steep waves, and the forces caused by water on the deck and deck-in-water that may occur in extreme waves. These phenomena are discussed in detail and their mathematical models are presented. They includes the modeling of water shipping on and off the weather deck, the dynamic effects of water trapped on deck with the volume changing during motions, and the effects of deep immersion of the deck.
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