倾角函数的无奇点计算

The non-singular-point computation of inclination functions

该文建立了倾角函数的递推计算关系,对任意的轨道倾角(0≤i<180),实现了倾角函数及其导数的快速无奇点计算,可供卫星动力学中的无奇点根数摄动计算使用.其稳定性与Gooding方法相当;其精度在180阶之内优于10-12;其计算速度比Gooding方法约快20～30倍.

The paper establishes a recursion relation about inclination functions, which can be used to compute the inclination function and its derivative for any inclination. The method avoids the difficulty of singular point when inclination is zero. It is valuable when we calculate the perturbation in satellite dynamics. The stability of the method is comparably with Gooding’s method, while its accuracy is better than 10-12 when the order is less than 180. Significantly, the speed of the method is much faster than Gooding’s about 20–30 times.