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For developed irregular waves, wave heights or wave amplitudes are gained using the wave spectrums. Based on the hypothesis of Froude-Krylov, ship shape is predigested box. Wave forces and moments to ship motion can be calculated. They are added in the motion mathematical models, and ship six degrees of freedom mathematical models are given. Using the fourth order Runge — Kutta integration method solves differential equations. The mathematical models are applied to Full Mission Ship Handling Simulator. Six degrees of freedom of the ship: the location, attitude and speed and acceleration are passed to the other modules in the navigation simulator, in order to achieve interaction between human and computer. As an example, a cargo ship that its displacement is ten thousand tons are simulated in three sea states, the time histories of motion are good and the viewing scene is very vivid. The results are shown that the mathematical models can meet the engineering demands. [ABSTRACT FROM PUBLISHER]