大地测量与地球动力学2011，Vol.31Issue(4)：94-98,5.
基于第二类椭圆积分的子午线弧长公式变换及解算
CALCULATING MERIDIAN ARC LENGTH BY TRANSFORMING ITS FORMULAE INTO ELLIPTIC INTEGRAL OF SECOND KIND
摘要
Abstract
A new idea that by transforming the meridian arc length formula into two other forms was put for-wand, which are expressed by the elliptic integrals of the second kind, they were named as " Form Ⅰ " and " Form Ⅱ ". In " Form Ⅰ " , the meridian arc length formula is represented as the sum of a rational function and the elliptic integrals of the second kind by the geodetic latitude parameter, which establishs the function relations between the meridian arc length and the elliptic integrals of the second kind. Analogously, taking the reduced latitude as an independent variable, the " Form Ⅱ " formula give a simpler form of the meridian arc length formula in terms of the elliptic integrals of the second kind. On these bases of theoretical analysis, the computer program is compiled in MATLAB by calling the Elliptic E(x, k) Function to calculate the meridian arc length. It was proved that this method improved greatly the accuracy and efficiency of previous calculation. Moreover, the meridian arc length of CGCS2000 was also calculated based on the principle that provided. The results indicate that the "Form Ⅰ " and " Form Ⅱ " formula are simpler and more suitable for series expansions and the realization on computer than the classical form. Furthermore, it perfects the meridian theory.关键词
子午线弧长/公式变换/椭圆积分/大地纬度/归化纬度Key words
meridian arc length/formula transformation/elliptic integrals/geodetic latitude/reduced latitude分类
天文与地球科学引用本文复制引用
过家春,赵秀侠,徐丽,田劲松,高飞..基于第二类椭圆积分的子午线弧长公式变换及解算[J].大地测量与地球动力学,2011,31(4):94-98,5.基金项目
国家自然科学基金(40771117) （40771117）
国家农业信息化工程技术研究中心开放课题(KF2010W40-046) （KF2010W40-046）
