Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit : analytic extension and numerical validation

In the research filed of nonlinear dynamical system theory it is well known that a homoclinic/heteroclinic point leads to unpredictable motions, such as chaos. Melnikov’s method enables us to judge whether the system has a homoclinic/heteroclinic orbit. Therefore, in order to assess a vessels safety against capsizing, Melnikov’s method has been applied for the investigations of chaos that appears in beam sea rolling. This is because chaos is closely related to capsizing incidents. In a previous paper 1), the formula to predict the capsizing boundary by applying Melnikov’s method to analytically obtain the non-Hamiltonian heteroclinic orbit, was proposed. However, in that paper, limited numerical investigation had been carried out. Therefore further comparative research between the analytical and numerical results is conducted, with the result being that the formula is validated.

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