MODIFIED APPROACH FOR THE APPLICATION OF FOKKER-PLANK EQUATION TO THE NONLINEAR SHIP MOTIONS IN RANDOM WAVES.

An analytical method for the study of transient behavior as well as the stationary solution of nonlinear ship motion in random waves is presented. The problem of rolling motion of a ship traveling in oblique random waves is considered for the purpose of illustrating the method. The presence of nonlinear damping and restoration terms of general form is allowed. Differential equations which govern the propagation of the expected value and the variance of the motion in this case are derived, using the Fokker-Plank equation. The results are specialized to the case of a ship rolling in beam waves. Results are compared with similar results obtained by other methods. This method gives the exact stationary solution when the damping is linear.