依不同纬度变量的子午线弧长正反解公式的级数展开

doi:10.11947/j.AGCS.2016.20140575

测绘学报 ›› 2016, Vol. 45 ›› Issue (5): 560-565.doi: 10.11947/j.AGCS.2016.20140575

依不同纬度变量的子午线弧长正反解公式的级数展开

过家春^1,2,3, 李厚朴⁴, 庄云玲¹, 李大军², 吴艳兰³

1. 安徽农业大学理学院, 安徽合肥 230036;
2. 东华理工大学江西省数字国土重点实验室, 江西南昌 330013;
3. 安徽大学资源与环境工程学院, 安徽合肥 230601;
4. 海军工程大学导航工程系, 湖北武汉 430033

收稿日期:2014-11-05 修回日期:2015-05-15 出版日期:2016-05-20 发布日期:2016-05-30
通讯作者: 吴艳兰 E-mail:wylmq@sina.com
作者简介:过家春(1981-),男,博士生,副教授,研究方向为大地测量学。E-mail: guojiachun@ahau.edu.cn
基金资助:
国家自然科学基金(41504031; 41571441);东华理工大学江西省数字国土重点实验室开放研究基金(DLLJ201507)

Series Expansion for Direct and Inverse Solutions of Meridian in Terms of Different Latitude Variables

GUO Jiachun^1,2,3, LI Houpu⁴, ZHUANG Yunling¹, LI Dajun², WU Yanlan³

1. School of Science, Anhui Agricultural University, Hefei 230036, China;
2. Jiangxi Province Key Lab for Digital Land, East China Institute of Technology, Nanchang 330013, China;
3. School of Resources and Environmental Engineering, Anhui University, Hefei 230601, China;
4. Department of Navigation, Naval University of Engineering, Wuhan 430033, ChinaAbstract

Received:2014-11-05 Revised:2015-05-15 Online:2016-05-20 Published:2016-05-30
Supported by:
The National Natural Science Foundation of China (Nos. 41504031;41571441);Foundation of Jiangxi Province Key Lab for Digital Land (No. DLLJ201507)

摘要/Abstract

摘要： 推导了以归化纬度、地心纬度解算子午线弧长的展开公式,同时又根据拉格朗日反演定理,得到了由子午线弧长反解归化纬度、地心纬度的直接公式。该组公式与子午线弧长正反解公式的大地纬度表达在结构形式上保持一致,进一步揭示了子午线弧长同3种纬度变量之间的内在联系。分析表明,基于归化纬度的子午线弧长解算与大地主题解算方法具有理论上的统一性,正反解精度均高于传统基于大地纬度的展开。

关键词: 子午线弧长, 级数展开, 大地纬度, 归化纬度, 地心纬度

Abstract: Formulas for direct solutions of meridian written by the reduced and geocentric latitudes respectively were derived by series expansion. Meanwhile, according to Lagrange inversion theorem, formulas for inverse solutions of the issue were also expressed in terms of the same latitudes. These two formulas were structurally consistent with that expressed by geodetic latitude ones. In these sets of formulas, internal connection between meridian and three different types of latitude were realized. Analysis and numerical calculation showed that the direct and inverse meridional solution with reduced latitude was of higher precision than that with geodetic latitude, and furthermore, there had a unified theory between meridian theory and classical geodetic problems expressed by reduced latitude.

Key words: meridian arc length, series expansion, geodetic latitude, reduced latitude, geocentric latitude

中图分类号:

P226

过家春, 李厚朴, 庄云玲, 李大军, 吴艳兰. 依不同纬度变量的子午线弧长正反解公式的级数展开[J]. 测绘学报, 2016, 45(5): 560-565.

GUO Jiachun, LI Houpu, ZHUANG Yunling, LI Dajun, WU Yanlan. Series Expansion for Direct and Inverse Solutions of Meridian in Terms of Different Latitude Variables[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(5): 560-565.

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依不同纬度变量的子午线弧长正反解公式的级数展开

Series Expansion for Direct and Inverse Solutions of Meridian in Terms of Different Latitude Variables

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