等量纬度展开式的新解法

对地图投影学中经常遇到的等量纬度正反解展开式进行了新的研究。借助M athem atica计算机代数系统强大的数学分析功能,给出了新的正解公式,发现并纠正了前人正解公式中的错误;并且以此为基础,导出了用第一偏心率幂级数形式表示的反解展开式和三种主要的参考椭球下的实用反解计算式。本文研究表明计算机代数系统的应用不但极大地提高了公式推演的效率和准确度,而且反解系数从此可以表示为更简单和更便于记忆的符号形式。

A New Solution to Expansions of Conformal Latitude

The expansions of conformal latitude in map projection are studied in this paper.With the help of the powerful computer algebra system,a new forward expansion of conformal latitude is derived,meanwhile some mistakes that once were made in the previous forward expansion are pointed out and corrected.Based on these,the inverse expansion is given in terms of a power series of the first eccentricity.The practical formulations are also provided under the three major referenced ellipsoid.The investigation in the paper shows that the application of computer algebra system in map projection not only improves the efficiency and accuracy of formulations but also gives out some symbolic expressions of the inverse expansions which are much simpler and more convenient to memorize.