CALCULATING MERIDIAN ARC LENGTH BY TRANSFORMING ITS FORMULAE INTO ELLIPTIC INTEGRAL OF SECOND KIND
Guo Jiachun 1) ; Zhao Xiuxia 2) ; Xu Li 1) ; Tian Jinsong 1) ; and Gao Fei 3)
1)School of Science,Anhui Agricultural University, Hefei 230036;2)School of Resources and Environmental Engineering, Anhui University, Hefei 230039;3)School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009
Abstract：A new idea that by transforming the meridian arc length formula into two other forms was put forwand, which are expressed by the elliptic integrals of the second kind, they were named as “FormⅠ” and “FormⅡ”. In “FormⅠ”, the meridian arc length formula is represented as the sum of a rational function and the elliptic integrals of the second kind by the geodetic latitude parameter, which establishs the function relations between the meridian arc length and the elliptic integrals of the second kind. Analogously, taking the reduced latitude as an independent variable, the “FormⅡ” formula give a simpler form of the meridian arc length formula in terms of the elliptic integrals of the second kind. On these bases of theoretical analysis, the computer program is compiled in MATLAB by calling the Elliptic E(x, k) Function to calculate the meridian arc length. It was proved that this method improved greatly the accuracy and efficiency of previous calculation. Moreover, the meridian arc length of CGCS2000 was also calculated based on the principle that provided. The results indicate that the “FormⅠ” and “FormⅡ” formula are simpler and more suitable for series expansions and the realization on computer than the classical form. Furthermore, it perfects the meridian theory.
Guo Jiachun ,Zhao Xiuxia ,Xu Li et al. CALCULATING MERIDIAN ARC LENGTH BY TRANSFORMING ITS FORMULAE INTO ELLIPTIC INTEGRAL OF SECOND KIND[J]. jgg, 2011, 31(4): 94-98.
