The motions of a ship in waves are expressed as linear responses to arbitrary exciting forces by means of a convolution integral. Frequency-independent nonlinearities are considered to be part of the arbitrary forces. The method is used to numerically simulate the sway, roll, and yaw motions of a ship model in waves with nonlinear roll damping coefficient and an autopilot. The agreement of the simulation with experimental results is quite reasonable. This method is restricted neither to these modes of motion nor to these nonlinearities; it can be used for all six modes of motion and any frequency-independent nonlinearity.

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