摘要
针对子午线弧长反解计算过于繁琐的问题 ,文中利用复合函数的求导法则 ,变换变量进行幂级数展开 ,在近似情况下给出了通项公式 ,并严密推导了幂级数展开式。又设定子午线弧长反解公式的形式 ,利用Hermite插值原理得出各参数。用各方法得出的公式全部采用e2 的幂级数形式给出 ,可操作性、可重复性、唯一性都比较好。经试算其精度在千分之一秒以上 ,可提供实际使用。
Making use if derivative rule of complex functions, this paper describes how to compute a foot point Latitude in ellipsoidal geodesy by Taylor expansion. As an important theoretical result, the paper also presents the general expression for the foot point latitude expansion. For comparison, based on the principle of Hermite interpolation, we can obtain each parameter of the formula. Each formula is given in form of series of e 2. The numerical investigation shows that the formulas described in the paper is sufficiently accurate up to 0.001″. It can satisfy practice utilization.
出处
《测绘学院学报》
2000年第3期167-171,共5页
Journal of Institute of Surveying and Mapping
关键词
椭球大地测量
子午线弧长反解
幂级数展开
ellipsoidal geodesy
foot point latitude
taylor expansion
Hermite interpolation
