Abstract This paper investigates the position of the instantaneous center of rotation in pitch response of a moored vessel submitted to regular head waves. The vessel is assumed to respond only in surge, heave and pitch, which allows a 2D approach in the x-z plane due to symmetry. The concept is formalized via an analytical approach in a previous study, showing that even though this point is time dependent it will always be located along a well-defined straight line in space for a moored vessel submitted to linear regular head waves. This study presents an analytical formulation to describe the distribution of these points along the straight line following a Cauchy probability density function. The concept of the Most Often Instantaneous Rotation Center in Pitch is introduced as the peak of said probability density function, which might arise as an interesting tool for quickly estimating the points of minimum amplitude of motion of a moored vessel submitted to head regular waves during one cycle. The paper also presents numerical data obtained through commercial software based on linear potential theory as well as experimental data from tests performed in a narrow wave channel to validate the proposed approach.

中文翻译：

---

锚泊船舶顺向规则波浪的俯仰瞬时旋转中心及其空间分布的进一步研究

摘要 本文研究了锚泊船舶在常规顶浪作用下的俯仰响应中瞬时旋转中心的位置。假定船舶仅在涌浪、升沉和俯仰中响应，由于对称性，这允许在 xz 平面中进行 2D 方法。该概念是通过先前研究中的分析方法形式化的，表明即使该点与时间有关，但它始终位于空间中一条明确定义的直线上，以便停泊船只受到线性规则波头波的影响。本研究提出了一种分析公式来描述这些点沿柯西概率密度函数沿直线的分布。音高中最常瞬时旋转中心的概念被引入为所述概率密度函数的峰值，这可能会作为一种有趣的工具出现，用于快速估计在一个周期内遇到规则波浪的系泊船舶的最小运动幅度点。本文还介绍了通过基于线性势理论的商业软件获得的数值数据以及在窄波通道中进行的测试的实验数据，以验证所提出的方法。