The nonlinear dynamics of ship motions: a field overview and some recent developments

Abstract

This opening article of the issue is intended to provide a review of the eld of nonlinear ship dynamics and to demonstrate the importance of the subject in the context of naval architecture. A list of relevant research topics that have received attention in recent years is included in the rst section of the paper. This sets the scene for a brief discussion about the content and contribution of the articles that make up the Theme Issue. In order to facilitate understanding by non-specialists, we include an outline of the general concepts of nonlinear dynamics. Furthermore, we provide a detailed review of the evolution of ship research of the considered type since the 1970s, including a rather lengthy bibliography. We discuss the latest ideas about ship capsize and we include a special section summarizing the recent advances with regard to the mechanisms of ship capsize in astern seas. We close the article by o¬ering some ideas about future directions for research.

Geometry of escaping dynamics in nonlinear ship motion

“…(b) Shows the total energy as contour lines on the configuration space (x, y) for different values above and below the critical energy E e . potential into unity and the original coordinates can always be recovered using the transformation (2). We note that equations 3 are identical to those derived by Ref.…”

“…However, the results from linear analysis only remain true for small amplitude motion and underestimate the critical conditions leading to capsize, which are primarily large amplitude, complicated nonlinear phenomena [1]. The primary objective of analyzing such models for different sea states is to generate initial conditions that lead to imminent capsize, or predict a range of parameter values that should be avoided to retain stability [2]. These models are typically analyzed using the computational and semi-analytical approaches that use the geometric features of the phase space such as the basin of attraction, and basin boundary.…”

Chaotic Dynamics in the Planar Gravitational Many-Body Problem with Rigid Body Rotations

“…The nonintegrable part of the Hamiltonian comes from the gravitational torque applied to the body, specifically for orbits which are non-circular as will be shown, similar to the Beletsky equation for non-zero orbit eccentricity Burov (1984); Celletii & Sidorendko (2008). The approach has been used to find homoclinic or heteroclinic chaos in a variety of systems Lin (1990); Hogan (1992); Yagasaki (1994); Spyrou & Thompson (2000); Zhang et al (2009Zhang et al ( , 2010 and has also been used to assist in the control of such chaos Chacon (2006). The method has been applied to homoclinic orbits corresponding to elliptic functions Belhaq et al (2000).…”

Multi-phase SPH modelling of air effect on the dynamic flooding of a damaged cabin

“…What's worse, these complex fluid flows are coupled with the nonlinear motion of the ship hull [2,3], so it is very difficult to forecast the complicate hydrodynamic process. During the flooding process, the dynamics of the air flow play a dominant role and compromise the stability of the damaged ship, which may lead to severe consequence [4] and warrants thorough study.…”