|
|||||
|
|
| 复变函数表示的高斯投影非迭代公式 | |
| 引用本文： | 李厚朴,王瑞,边少锋.复变函数表示的高斯投影非迭代公式[J].海洋测绘,2009,29(6):17-20. |
| 作者姓名： | 李厚朴 王瑞 边少锋 |
| 作者单位： | 1. 海军工程大学,导航工程系,湖北,武汉,430033 2. 海军工程大学,导航工程系,湖北,武汉,430033;海军司令部,航海保证部,天津,300042 3. 海军工程大学,导航工程系,湖北,武汉,430033;中国科学院,测量与地球物理研究所,湖北,武汉,430077 |
| 基金项目： | 国家自然科学基金资助项目，国家杰出青年科学基金资助项目 |
| 摘 要： | 借助复数理论讨论了高斯投影的复变函数表示。引入了等量纬度反解的直接展开式，借助计算机代数系统Mathematica推导出了子午线弧长与等量纬度之间的关系式，并将其拓展至复数域，导出了形式紧凑、结构简单的高斯投影正反解非迭代公式，并在此基础上给出了适合计算机计算的表达式及其相关系数在不同参考椭球下的数值形式。算例结果表明本文公式计算精度在10^-6s以上，可供实际使用。 |
| 关 键 词： | 高斯投影 复变函数 非迭代公式 计算机代数系统 |
The Non-iterative Formulae of Gauss Projection by Complex Numbers |
|
| LI Hou-pu,WANG Rui,BIAN Shao-feng.The Non-iterative Formulae of Gauss Projection by Complex Numbers[J].Hydrographic Surveying and Charting,2009,29(6):17-20. | |
| Authors: | LI Hou-pu WANG Rui BIAN Shao-feng |
| Institution: | 1. Department of Navigation, Naval University of Engineering, Wuhan, Hubei ,430033 ; 2. Navigation Guarantee Department of Naval Headquarters,Tianjin,300042 ; 3. Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan, Hubei ,430077 ) |
| Abstract: | Gauss projection is discussed with the help of complex numbers theory. The direct expansion of the conformal latitude＇ s inverse solution is introduced in this paper. Expressions that illuminate the relationship between meridian arc and conformal latitude are derived with the help of computer algebra system Mathematica. After developing them into complex numbers domain,non-iterative formulae with a very concise form for Gauss projection＇ s forward and inverse transformations are also available. Based on these, expressions that can satisfy computer calculation requirement and their coefficients＇ numerical forms under different referenced ellipsoids are both given. Numerical examples show that the precision of these formulae is sufficiently accurate up to 10^-6 s and can satisfy practical use. |
| Keywords: | Gauss projection complex numbers non-iterative formulae computer algebra system |
| 本文献已被 维普 万方数据 等数据库收录！ | |
| 点击此处可从《海洋测绘》浏览原始摘要信息 | |
| 点击此处可从《海洋测绘》下载免费的PDF全文 | |