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Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit: analytic extension and numerical validation |
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| Authors: | Atsuo Maki Naoya Umeda Tetsushi Ueta |
| Institution: | 1. Graduate School of Maritime Sciences, Kobe University, 5-1-1 Fukae-Minami, Higashinada, Kobe, 658-0022, Japan 2. Naval System Research Centre, Technical Research & Development Institute, Ministry of Defence, 2-2-1 Nakameguro, Meguro, Tokyo, 153-8630, Japan 3. Department of Naval Architecture and Ocean Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka, 565-0971, Japan 4. Centre for Advanced Information Technology, Tokushima University, Minami-Josanjima, Tokushima, 770-8506, Japan |
| Abstract: | In the research field 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 vessel's safety with respect to capsizing, Melnikov’s method has been applied for investigations of the chaos that appears in beam sea rolling. This is because chaos is closely related to capsizing incidents. In a previous paper (Maki et al. in J Mar Sci Technol 15:102–106, 2010), a 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, only limited numerical investigation was 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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