大地线极点归化纬度的迭代求解法

An iterative method for solving the naturalized latitude of the geodetic pole

针对大地线极点归化纬度求解问题,通过利用两个白塞尔微分方程,结合克莱劳定理正弦形式和球面直角三角形Napier通用规则,推演得到白塞尔球面弧长σ和球面经差ω的归化纬度表达式,结合表达式得到椭球面经差和白塞尔球面弧长的微分关系式。通过已经推得关系式,引入三角函数,最终得到椭球面和白塞尔球面之间经度缩量的具体表达式和经度缩量之差的严密关系式。巧妙地分离了大地线流动点和最高点的归化纬度,得出大地线极点的归化纬度迭代计算式,最终求解大地线极点归化纬度。最后将此方法进行实际应用,与传统方法得出结果对比,证明此方法计算大地线极点归化纬度的可靠性。

This paper focuses on solving the problem of the naturalized latitude of the geodetic pole.By using two Bessel differential equations, and combining the sine form of Clairaut theorem and the general rule of the spherical right-angled triangle Napier, the arc length σ and the sphericallongitude ω of the Bessel spherical surface are deduced.The normalized latitude expression of the difference is combined with the expression to obtain the differential relationship between the longitude difference of the ellipsoid and the arc length of the Bessel spherical surface.By deducing the relational expression and introducing the trigonometric function, the specific expression of the longitude shrinkage between the ellipsoid surface the Bessel sphere and the strict relational expression of the difference between the longitude shrinkage are finally obtained.The naturalized latitude of the geodetic flow point and the highest point is cleverly separated, and the iterative calculation formula for the naturalized latitude of the geodetic pole is obtained, and the naturalized latitude of the geodetic pole is finally solved.Finally, the method is applied in practice compared with the results obtained by the traditional method, which proves the reliability of this method in calculating the naturalized latitude of the earth line pole.