ロル型転覆方程式のカオスとフラクタル

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A ship with flooded water into some damaged compartments, or with shipped water on deck has often negative GM, which means unstable equilibrium at an upright condition, and is stable at some heel angle. A capsize equation for such a ship is named a loll type capsize equation, or two well capsize equation because the potential function has the two well. On the basis of the recently developed nonlinear dynamical systems theory, authors have been studying the ordinary capsize equation of one well type. Even for the simplest capsize equation with the one well potential, many mysterious nonlinear phenomena have been observed by the numerical studies. For the capsize equation with the two well potential, similar numerical studies have been carried out. As a result, many different phenomena have been observed in the bifurcation diagrams, time histories, phase portraits, chaotic attractors, basin boundary metamorphoses and capsize boundaries in the control space. In the bifurcation diagrams, a wide range of the chaos with several windows having the finite period such as 3T or 5T is observed. A complicated and splendid chaotic attractor is also observed, while in the one well type there exists only a simple chaotic attractor of the folded band. Safe basin in the initial value plane is eroded in a different manner from one well type. The boundaries between capsize and non-capsize regions in the control space have another fractal like features. In this paper such complicated and mysterious phenomena are described, but the mechanism of such phenomena, and the totality of the outstructure are not examined, except an approximate bifurcation analysis and a Melnikov analysis. In order to clarify the difference between one and two well equations, the invariant manifold analysis should be done. Applications to the safety criterion should also be pursued.
社団法人日本船舶海洋工学会の論文
1992-03-29

ロル型転覆方程式のカオスとフラクタル

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