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中文摘要：
采用经典Kepler根数描述天体的基本运动方程时,若出现近圆或近赤道情况,将导致一系列的不确定性,即奇点问题。由于导致这类数学奇点的原因是基本根数变量的选择不当,因此有针对性地选择无奇点根数可以解决这一问题。在前人提出的改进的第二类无奇点根数的基础上,给出详细的星历计算和轨道计算推导过程。并且通过摄动运动方程形式分析以及数值计算对改进根数进行了验证。
英文摘要：
Celestial motions are usually described by the Kepler elements. Under the conditions of small eccentricity and （or） small inclination, an apparent loss of accuracy due to the singularity came out. Therefore, several kinds of no-singularity variables were presented to avoid the Kepler elements at these moments. Based on the second class of no singularity variables, the formula and procedures were given to compute the ephemeris and orbits using the improved elements. The effects of no-singularity were demonstrated and the accuracy by the perturbed motion equations of the improved elements was validated through the simulations.
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