[1] TORGE W. Geodesy[M]. 3rd ed. Berlin: Walter de Gruyter, 2001: 91-98. [2] 孔祥元, 郭际明, 刘宗泉. 大地测量学基础[M]. 武汉: 武汉大学出版社, 2001: 64-73. KONG Xiangyuan, GUO Jiming, LIU Zongquan. Foundation of Geodesy[M]. Wuhan: Wuhan University Press, 2001: 64-73. [3] HELMERT F R. Die Mathematischen und Physikalischen Theorien der H heren Geodäsie[M]. Leipzig: Druck und Verlag von B.G. Teubner, 1880: 46-48. [4] DEAKIN R E, HUNTER M N. Geometric Geodesy: Part A[R]. Melbourne: School of Mathematical & Geospatial Science, RMIT University, 2010: 60-77. [5] 程鹏飞, 成英燕, 文汉江, 等. 2000国家大地坐标系实用宝典[M]. 北京: 测绘出版社, 2008: 147-148. CHENG Pengfei, CHENG Yingyan, WEN Hanjiang, et al. Practical Manual on CGCS 2000[M]. Beijing: Surveying and Mapping Press, 2008: 147-148. [6] 刘正才. 子午线弧长公式的简化及通用高斯投影计算程序介绍[J]. 测绘工程, 2001, 10(1): 55-56, 62. LIU Zhengcai. Simplification of Formula of Meridian Arc Length & Program of General Gauss Projection[J]. Engineering of Surveying and Mapping, 2001, 10(1): 55-56, 62. [7] 易维勇, 边少锋, 朱汉泉. 子午线弧长的解析型幂级数确定[J]. 测绘学院学报, 2000, 17(3): 167-171. YI Weiyong, BIAN Shaofeng, ZHU Hanquan. Determination of Foot Point Latitude by Analytic Positive Serires[J]. Journal of Institute of Surveying and Mapping, 2000, 17(3): 167-171. [8] 刘仁钊, 伍吉仓. 任意精度的子午线弧长递归计算[J]. 大地测量与地球动力学, 2007, 27(5): 59-62. LIU Renzhao, WU Jicang. Recursive Computation of Meridian Arc Length with Discretionary Precision[J]. Journal of Geodesy and Geodynamics, 2007, 27(5): 59-62. [9] BIAN S F, CHEN Y B. Solving an Inverse Problem of a Meridian Arc in Terms of Computer Algebra System[J]. Journal of Surveying Engineering, 2006, 132(1): 7-10. [10] 牛卓立. 以空间直角坐标为参数的子午线弧长计算公式[J]. 测绘通报, 2001(11): 14-15. DOI:10.3969/j.issn.0494-0911.2001.11.006. NIU Zhuoli. Formulae for Calculation of Meridian Arc Length by the Parameters of Space Rectangular Coordinates[J]. Bulletin of Surveying and Mapping, 2001(11): 14-15. DOI: 10.3969/j.issn.0494-0911.2001.11.006. [11] 刘修善. 计算子午线弧长的数值积分法[J]. 测绘通报, 2006(5): 4-6. DOI:10.3969/j.issn.0494-0911.2006.05.002. LIU Xiushan. Numerical Integral Method of Calculating Meridian Arc Length[J]. Bulletin of Surveying and Mapping, 2006(5):4-6. DOI:10.3969/j.issn.0494-0911.2006.05.002. [12] BOWRING B R, New Equations for Meridional Distance[J]. Bulletin Géodésique, 1983, 57(1-4): 374-381. [13] KAWASE K. A General Formula for Calculating Meridian Arc Length and Its Application to Coordinate Conversion in the Gauss-Krüger Projection[J]. Bulletin of the Geospatial Information Authority of Japan, 2011, 59: 1-13. [14] 过家春, 赵秀侠, 徐丽, 等. 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. GUO Jiachun, ZHAO Xiuxia, XU Li, et al. Calculating Meridian Arc Length by Transforming Its Formulae into Elliptic Integral of Second Kind[J]. Journal of Geodesy and Geodynamics, 2011, 31(4): 94-98. [15] 过家春. 基于第二类椭圆积分的子午线弧长反解新方法[J]. 大地测量与地球动力学, 2012, 32(3): 116-120. GUO Jiachun. New Method for Inverse Solution of Meridian Based on Elliptic Integral of Second Kind[J]. Journal of Geodesy and Geodynamics, 2012, 32(3): 116-120. [16] 过家春. 子午线弧长公式的简化及其泰勒级数解释[J]. 测绘学报, 2014, 43(2): 125-130. DOI: 10.13485/j.cnki.11-2089.2014.0017. GUO Jiachun. A Simplification of the Meridian Formula and Its Taylor-series Interpretation[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(2): 125-130. DOI: 10.13485/j.cnki.11-2089.2014.0017. [17] 李忠美, 李厚朴, 边少锋. 常用纬度差异极值符号表达式[J]. 测绘学报, 2014, 43(2): 214-220. DOI: 10.13485/j.cnki.11-2089.2014.0031. LI Zhongmei, LI Houpu, BIAN Shaofeng. Symbolic Expressions of Difference Extrema between Regular Latitudes[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(2): 214-220. DOI: 10.13485/j.cnki.11-2089.2014.0031. [18] 孙群, 杨启和. 底点纬度解算以及等量纬度和面积函数反解问题的探讨[J]. 解放军测绘学院学报, 1985(2): 64-75. SUN Qun, YANG Qihe. The Research on the Computation of the Foot-point Latitude and the Inverse Solution of Isometric Latitude and Area Function[J]. Journal of PLA of Surveying and Mapping, 1985(2): 64-75. [19] 李厚朴, 边少锋. 高斯投影的复变函数表示[J]. 测绘学报, 2008, 37(1): 5-9. DOI: 10.3321/j.issn:1001-1595.2008.01.002. LI Houpu, BIAN Shaofeng. The Expressions of Gauss Projection by Complex Numbers[J]. Acta Geodaetica et Cartographica Sinica, 2008, 37(1): 5-9. DOI: 10.3321/j.issn:1001-1595.2008.01.002. [20] DORRER E. From Elliptic Arc Length to Gauss-Krüger Coordinates by Analytical Continuation[M]//GRAFAREND E W, KRUMM F W, SCHWARZE V S. Geodesy-The Challenge of the 3rd Millennium. Berlin: Springer, 2003: 293-298. [21] LEE L P. Some Conformal Projections Based on Elliptic Functions[J]. Geographical Review, 1965, 55(4): 563-580. [22] BERMEJO-SOLERA M, OTERO J. Simple and Highly Accurate Formulas for the Computation of Transverse Mercator Coordinates from Longitude and Isometric Latitude[J]. Journal of Geodesy, 2009, 83(1): 1-12. [23] SJÖBERG L E. New Solutions to the Direct and Indirect Geodetic Problems on the Ellipsoid[J]. Zeitschriftfuer Vermessungswesen, 2006, 131: 35-39. [24] SJÖBERG L E, SHIRAZIAN M. Solving the Direct and Inverse Geodetic Problems on the Ellipsoid by Numerical Integration[J]. Journal of Surveying Engineering, 2012, 138(1): 9-16. [25] 张彦博. 等弧长椭圆时间分割插补算法[J]. 机床与液压, 2005(7): 41, 110. ZHANG Yanbo. Equal Arc Length Time Dividing Interpolation of Ellipse[J]. Machine Tool & Hydraulics, 2005(7): 41, 110. [26] 刘有余, 韩江, 夏链等. 外啮合椭圆齿轮多方案插齿三维仿真与分析[J]. 机械科学与技术, 2014, 33(7): 1031-1035. LIU Youyu, HAN Jiang, XIA Lian, et al. 3D-simulation and Analysis of Multiple Slotting External Elliptic Gears[J]. Mechanical Science and Technology for Aerospace Engineering, 2014, 33(7): 1031-1035. [27] WOLFRAM S. The Mathematica Book[M]. 5th ed. Champaign: Wolfram Media Inc., 2003. [28] ABRAMOWITZ M, STEGUN I A. Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables[M]. New York: Dover Publications Inc., 1972: 14-16. [29] WEISSTEIN E W, "Series Reversion" from MathWorld: A Wolfram Web Resource[DB/OL].[2015-05-14]. http://mathworld.wolfram.com/SeriesReversion.html. |