依不同纬度变量的常用曲率半径的直接展开式  

Direct Expansions for Common Curvature Radii in Terms of Different

作　　者：李晓勇 李厚朴[1] 刘国辉 边少锋[1] LI Xiaoyong;LI Houpu;LIU Guohui;BIAN Shaofeng(College of Electrical Engineering,Naval University of Engineering,Wuhan 430033,China;Chart Information Center,Tianjin 300450,China)

机构地区：[1]海军工程大学电气工程学院导航工程教研室,湖北武汉430043 [2]海图信息中心,天津300450

出　　处：《测绘地理信息》2024年第2期45-50,共6页Journal of Geomatics

基　　金：国家自然科学基金(41871376,41971416);国家优秀青年科学基金(42122025)。

摘　　要：通过计算机代数系统Mathematica推导出了以地心纬度、归化纬度为变量的卯酉圈曲率半径、子午圈曲率半径和平均曲率半径的直接表达式,该表达式适用于任何椭球参数,具有通用性。并将常规的基于第一偏心率e表示的公式改写为基于第三扁率n表示的公式,以2000国家大地坐标系(China Geodetic Coordinate System2000,CGCS2000)椭球为例分析了推导出的直接表达式的精确性和可靠性。经分析可得,常用曲率半径展开至e^(6)或n^(3)时,既能满足大地测量学要求的精度,也更为紧凑简练,一定程度上提高了地图投影的计算效率。With the computer algebra system Mathematica,the direct calculation formulas of radius of curvature in prime vertical,meridian radius of curvature,mean radius of curva ture are derived,which take geocentric latitude and reduced latitude as variables.The expressions can be applied to any ellipsoid parameter for their universality.The conventional formula based on the first eccentricity e is rewritten to the formula based on the third oblate n,and China Geodetic Coordinate System 2000(CGCS2000)ellipsoid is used to analyze the accuracy and reliability of the derived direct expressions.The analysis result shows that when the curvature radi are expanded to e^(6)or n^(3),the accuracy of geodesy can be satisfied,and the calculation efficiency of map projection can be improved to some extent.

关 键 词：子午圈曲率半径 卯酉圈曲率半径平均曲率半径 归化纬度 地心纬度 计算机代数系统 

分 类 号：P282[天文地球—地图制图学与地理信息工程]