标题： 浮体：关于静水效应的守恒性的一篇注记 显示英文标题

标题： Floating rigid bodies: a note on the conservativeness of the hydrostatic effects

摘要： 在拉格朗日力学的框架内，证明了作用在浮体上的静水力的保守性。 给出了相关静水势的显式表示。 利用所得拉格朗日量在纵荡、横荡和偏航运动下的不变性，结合Routh方法，将原始动力学问题转化为三个独立变量的简化问题。 这使得能够以合理的基础研究静水平衡，引入伪稳定性概念，即相对于简化问题的稳定性。 讨论了系统围绕伪稳定平衡构型的小振荡。 显示英文摘要

摘要： Within the framework of Lagrangian mechanics, the conservativeness of the hydrostatic forces acting on a floating rigid body is proved. The representation of the associated hydrostatic potential is explicitly worked out. The invariance of the resulting Lagrangian with respect surge, sway and yaw motions is used in connection with the Routh procedure in order to convert the original dynamical problem into a reduced one, in three independent variables. This allows to put on rational grounds the study of hydrostatic equilibrium, introducing the concept of pseudo--stability, meant as stability with respect to the reduced problem. The small oscillations of the system around a pseudo-stable equilibrium configuration are discussed.