扁球体水准面与水准椭球面形状差异的研究  

A Study of the Shape Difference between the Level Surfaces of the Oblate Spheroid and the Ellipsoid

作　　者：李厚朴[1] 边少锋[1,2] 

机构地区：[1]海军工程大学导航工程系,湖北武汉430033 [2]中国科学院测量与地球物理研究所,湖北武汉430077

出　　处：《测绘学报》2009年第2期95-100,共6页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(40644020,40774002);国家杰出青年科学基金(40125013)

摘　　要：对赫尔默特扁球与布隆斯扁球的水准面方程进行新的研究,借助计算机代数系统Mathematica,采用幂级数展开法推导其严密表达式,以此为基础,通过数值计算分析,揭示出这2种扁球体的水准面与水准椭球面的形状差异,澄清和改正前人对这一问题的认识。A new study of the level surface equations of Bruns＇ spheroid and Helmert＇s spheroid is carried out in this paper. With the help of the computer algebra systemMathematica, the strict expressions of the level surfaceequations are derived using the method of power series expansion. Based on these expressions, actual differences between level surfaces of oblate spheroids and the ellipsoid are illustrated visually through numerical calculation and analysis, and the knowledge in previous literatures about this problem are clarified and corrected.

关 键 词：扁球体 水准面方程 水准椭球 计算机代数系统 

分 类 号：P223[天文地球—大地测量学与测量工程]