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### 基于第二类椭圆积分的子午线弧长正反解新方法

• 收稿日期:2011-03-02 修回日期:2011-07-06 出版日期:2011-12-28 发布日期:2019-01-01
• 通讯作者: 过家春

### New Method for Direct and Inverse Solutions of Meridian Based on the Elliptic Integral of the Second Kind

• Received:2011-03-02 Revised:2011-07-06 Online:2011-12-28 Published:2019-01-01

Abstract: Based on the theory of the elliptic integral of the second kind, the meridian arc length formula was transformed into the Legendre’s canonical form for the elliptic integral of the second kind, so that the direct and inverse problems of Meridian could be solved by the elliptic integral of the second kind, and it revealed the essence of the problems. By the new method we described, the truth value of meridian arc length was calculated, and the computation efficiency was also further enhanced. On the other hand, an analytical method was offered to solve the inverse problem of Meridian. The new formula for inverse solution of Meridian was expressed by Maclaurin Series with constant coefficients that generated by the cosine function of reduced latitude. Numerical calculation indicated that the rate of convergence of the series is higher and the errors can be estimated accurately, thereby choosing the last term of the series easily in practical application. Theoretical analytics and application examples showed that the new method is more suitable for computer realization than the existing methods, and has a consolidated mathematical model suited for all earth ellipsoids.