A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation.Analytical expressions for the roll angle,velocity,accelerati...A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation.Analytical expressions for the roll angle,velocity,acceleration,and damping and restoring moments are derived using a modified approach of homotopy perturbation method(HPM).Also,the operational matrix of derivatives of ultraspherical wavelets is used to obtain a numerical solution of the governing equation.Illustrative examples are provided to examine the applicability and accuracy of the proposed methods when compared with a highly accurate numerical scheme.展开更多
基金The authors are thankful to Shri J.Ramachandran,Chancellor,Col.Dr.G.Thiruvasagam,Vice-Chancellor,Academy of Maritime Education and Training(AMET),Deemed to be University,Chennai,for their support.
文摘A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation.Analytical expressions for the roll angle,velocity,acceleration,and damping and restoring moments are derived using a modified approach of homotopy perturbation method(HPM).Also,the operational matrix of derivatives of ultraspherical wavelets is used to obtain a numerical solution of the governing equation.Illustrative examples are provided to examine the applicability and accuracy of the proposed methods when compared with a highly accurate numerical scheme.
