Mathematical Modeling of Nonlinear Roll Motion of Ships using Homotopy Perturbation Method

Abstract

Mathematical modelling of the nonlinear roll motion of a ship is discussed. The model is based on second- order nonlinear equations containing a nonlinear term related to damping and restoring moment. Analytical solution of the nonlinear equations is obtained using a modified homotopy perturbation method. For normal or irregular waves, roll angle, roll velocity, and moment of damping and restoring for the particular ship are also provided. A comparison of the theoretical approximation obtained via the proposed approach shows strong agreement with the numerical results.