LARHYSS Journal
Volume 19, Numéro 4, Pages 101-116
2022-12-07

Analytical Approach Of Two General Nonlinear Ship Motions In Time Domain



Authors : S Rekha . D Gowthaman . P Balaganesan . B Achour .

Abstract

Two nonlinear models of the roll motion of ships are discussed and analytically solved. Both models are second-order differential equations with nonlinear restoring and damping moments. A new approach to the homotopy perturbation method is applied to derive analytical expressions for the roll angle, velocity, acceleration and restoring and damping moments. The analytical results are validated by direct comparison with the fourth-order Runge‒Kutta method. The analytical approach of this paper can be efficiently extended to various vibrating dynamical models arising in mechanical systems.

Keywords

Mathematical modeling ; ship dynamics ; capsizing ; restoring and damping moments ; analytical solution

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