革新引力势分析：从克莱罗（Clairaut）到李群（Lie Groups）
Revolutionizing Gravitational Potential Analysis: From Clairaut to Lie Groups
AI总结：
本研究提出一种基于李群与指数映射的新理论，可推导流体天体受外力时大引力扰动与形状函数的精确微分方程，为高精度求解多极矩与Love数奠定基础。
摘要：
这篇快报提出了一种先进的全新理论，用于计算受外部潮汐力和旋转力作用的流体恒星与行星的密度、形状及引力场中的非线性牛顿流体静力学扰动。该理论采用李群方法，借助指数映射推导大引力场扰动和描述天体外形有限形变的形状函数的精确微分方程。这一方法为以任意所需精度对受作用天体的多极矩和Love数进行精确解析确定与数值计算奠定了基础。
英文摘要：
This letter introduces an advanced novel theory for calculating non-linear Newtonian hydrostatic perturbations in the density, shape, and gravitational field of fluid stars and planets subjected to external tidal and rotational forces. The theory employs a Lie group approach using exponential mappings to derive exact differential equations for large gravitational field perturbations and the shape function, which describes the finite deformation of the body's figure. This approach lays the foundation for the precise analytic determination and numerical computation of the induced body's multipole moments and Love numbers with any desired degree of accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
