新型大地坐标系中大地线的微分方程和微分式  

Differential Equations and Differential Relationships of Geodesic Lines in New Form of Geodetic Coordinate System

作　　者：施一民[1] 朱紫阳[2] 

机构地区：[1]同济大学测量与国土信息工程系 [2]广东省国土资源厅测绘院,广东广州510500

出　　处：《同济大学学报（自然科学版）》2007年第1期108-111,共4页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金资助项目(40471114)

摘　　要：应用微分几何和大地测量理论提出并推证了以新大地坐标为坐标参数的大地线的一阶、二阶微分方程及其各阶导数.为进行测地主题正反解,进行椭球面上的简便计算及应用于三维GIS建模奠定了理论基础.Based on the theory of the differential geometry and geodesy, the first and the second order differential equation and 1-3 order differential relationship based on the new geodetic coordinates are derived for the new form of geodetic coordinate system on the ellipsoidal surface. The given necessary condition expression for geodesic line is the same as that one by the Clairaut theorem in geodetic coordinate system. The first order differential relationship can also be derived from the Liouville formula on the differential geometry. It is useful for the direct and inverse solution of geodetic problem and applying to ellipsoidal surface and modeling for three dimensional GIS.

关 键 词：新型大地坐标系 大地方位角 测地坐标 微分方程 微分关系式 

分 类 号：P223[天文地球—大地测量学与测量工程]