A NON-LINEAR MATHEMATICAL MODEL OF ROLL MOTION OF SHIPS WITH A HIGHERORDER A POLYNOMIAL OF RIGHTING ARM

Abstract

A theoretical model of prediction of the rolling of the ship is discussed. The rolling motion of a ship
with exciting force has been defined as a nonlinear differential equation, taking into account the nonlinearity of
higher-order polynomial of righting arm. Approximate analytical solutions of the differential equation of roll
motion are solved using the modified homotopy perturbation method. The approximate analytical expression of
roll angle, velocity, acceleration restoring moment, and damping moment is obtained. Analytical solutions are
compared with numerical results( Matlab). A satisfactory agreement is noted.