船舶非线性横摇运动与混沌

本文以波浪尺度为变参数，通过平均化方法和范德坡变换，确定横摇运动的振动解随参数变化的定性情况；然后运用数值积分和胞映射相结合的方法，求得系统的多种形式的振动解。胞映射法能灵活地处理各种不同形式的吸引子，如谐振解、各阶亚谐解乃至混沌吸引子并能方便快速地求解。横摇运动的大量非线性特性，如吸引子共存，对称性破缺，周期倍化等现象都被观察到。多个吸引子共存时，吸引域往往具有复杂的结构。文中还给出了由一系列倍周期分岔导致的混沌运动。

NONLINEAR OSCILLATIONS AND CHAOS OF SHIP ROLLING MOTION

The quality of ship rolling dynamics changing with wave amplitude is analyzed through the Mean Method and the Van de Pol transformation. Moreover, the direct integrating method and the cell-map method are combined to obtain the various oscillation solutions. It is noticed that the cell-map method shows flexibility and potency in dealing with all kinds of periodical solutions. Many nonlinear characteristics of ship rolling, such as existence of multiple attractors, symmetric breaking, period doubling and so on, are observed. While multiple attractors exist, the structure of the attracting basin are often very complicated, implying the sensitivity to state value. The chaos caused by a sequences of period doubling is emphasized.