Modeling of Ship Roll Dynamics and Its Coupling with Heave and Pitch
In order to study the dynamic behavior of ships navigating in severe environmental conditions it is imperative to develop their governing equations of motion taking into account the inherent nonlinearity of large-amplitude ship motion. The purpose of this paper is to present the coupled nonlinear equations of motion in heave, roll, and pitch based on physical grounds. The ingredients of the formulation are comprised of three main components. These are the inertia forces and moments, restoring forces and moments, and damping forces and moments with an emphasis to the roll damping moment. In the formulation of the restoring forces and moments, the influence of large-amplitude ship motions will be considered together with ocean wave loads. The special cases of coupled roll-pitch and purely roll equations of motion are obtained from the general formulation. The paper includes an assessment of roll stochastic stability and probabilistic approaches used to estimate the probability of capsizing and parameter identification.
An investigation into the motion and stability behaviour of a RO-RO vessel
. Studies on motion response of a vessel is of great interest to researchers, since a long time. But intensive researches on stability of vessel during motion under dynamic conditions are few. A numerical model of vessel is developed and responses are analyzed in head, beam and quartering sea conditions. Variation of response amplitude operator (RAO) of vessel based on Strip Theory for different wave heights is plotted. Validation of results was done experimentally and numerical results was considered to obtain effect of damping on vessel stability. A scale model ratio of 1:125 was used which is suitable for dimensions of wave flume at National Institute of Technology Calicut. Stability chart are developed based on Mathieu‟s equation of stability. Ince-Strutt chart developed can help to capture variations of stability with damping.
Fractal basin boundaries
Abstract Basin boundaries for dynamical systems can be either smooth or fractal. This paper investigates fractal basin boundaries. One practical consequence of such boundaries is that they can lead to great difficulty in predicting to which attractor a system eventually goes. The structure of fractal basin boundaries can be classified as being either locally connected or locally disconnected. Examples and discussion of both types of structures are given, and it appears that fractal basin boundaries should be common in typical dynamical systems. Lyapunov numbers and the dimension for the measure generated by inverse orbits are also discussed.