Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit: analytic extension and numerical validation
Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit: analytic extension and numerical validation
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DOI：
10.1007/s00773-013-0244-z
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发表时间：
2014-03
影响因子：
2.6
通讯作者：
A. Maki;N. Umeda;T. Ueta
中科院分区：
文献类型：
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作者：
A. Maki;N. Umeda;T. Ueta
在非线性动力系统理论的研究领域中，一个同斜点/异斜点会导致不可预测的运动，如混沌。Melnikov的方法使我们能够判断系统是否具有同斜/异斜轨道。因此，为了评估船舶在倾覆方面的安全性，Melnikov方法已被应用于研究横摇海中出现的混沌。这是因为混乱与翻船事件密切相关。在之前的一篇论文中（Maki et al. In J Mar Sci Technol 15:10 02 - 106, 2010），提出了利用Melnikov方法解析得到非哈密顿异斜轨道来预测倾覆边界的公式。然而，在该论文中，只进行了有限的数值调查。因此，对解析结果和数值结果进行了进一步的对比研究，验证了公式的正确性。
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.