等距离纬度等量纬度和等面积纬度展开式

The Expansions of Rectifying Latitude,Conformal Latitude and Authalic Latitude

对数学制图学中经常遇到的等距离纬度、等量纬度和等面积纬度展开式进行新的研究。借助计算机代数系统强大的数学分析功能,给出这些纬度用偏心率幂级数形式表示的正解公式,并且以此为基础,给出纬度用偏心率幂级数形式表示的反解展开式,与以往数值形式表示的反解公式不同,这些反解展开式是以符号形式给出,研究表明计算机代数系统的应用不但极大地提高公式推演的效率和准确度,而且反解系数可以表示为更简单和更便于记忆的符号形式。

The Expansions of rectifying latitude, conformal latitude and authalic latitude in mathematical cartography is researched in the paper. With the help of the powerful computer algebra system, some more accurate expansions of these latitudes are derived. Based on these expansions, the inverse expansions of these latitudes are given in terms of a power series of the eccentricity. Being different from the previous numerical form, all these inverse expansions are symbolically expressed. The investigation in the paper shows that the application of computer algebra system in mathematical cartography not only improves the efficiency and accuracy of formulations but also gives out some more simple symbolic expressions of the inverse expansions.