Journal of Marine Science and Technology

, Volume 19, Issue 3, pp 257–264

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

• Atsuo Maki
• Naoya Umeda
• Tetsushi Ueta
Original article

## 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.

## Keywords

Melnikov’s method Beam seas Roll motion Non-Hamiltonian exact heteroclinic orbit

## Notes

### Acknowledgments

This research was partly supported by a Grant-in-Aid for Scientific Research of the Japan Society for Promotion of Science (No. 24360355). The authors express the sincere gratitude to the above organization. The authors are grateful to Mr. John Kecsmar from Ad Hoc Marine Designs, Ltd., for his comprehensive review of this paper as an expert in small craft technology and a native English speaker.

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