轨道要素奇异问题的改进四元数方法

摘要

The singularity problem of orbital elements for describing the orbital motion of the spacecraft can be solved by quaternion method. Due to the inherent double-value of the quaternion, it is difficult to select positive or negative value of the quaternion for the integration of the motion equation. The quaternion methodology with a modified constraint equation was introduced to describe Lagrange's planetary equations. The influence of the earth oblateness perturbation on the orbit of the geostationary satellite was researched. The results show that when the eccentricity is less than 1, the quaternion can be used to solve singularity problem caused by orbital elements. Compared with the modified equinoctial orbit elements, the quaternion has a clearer physical and geometrical interpretation. The variable motion equation with the quaternion can be calculated more simply and integrated more efficiently. In addition, the calculation error can also meet the requirements.%运用四元数方法可以在一定范围内解决描绘飞行器轨道运动时轨道要素的奇异问题.但四元数固有的双值性使得在对运动方程进行积分时,其正负选取很困难.为了解决这一问题,采用了改进约束方程的四元数方法,并用该方法描述了拉格朗日行星摄动方程,然后研究了地球扁率摄动对地球同步卫星轨道的影响.仿真结果表明:当偏心率小于1时,四元数可以很好地解决轨道要素奇异性问题.与改进的春分点轨道要素相比,四元数的方法有着更加明确的物理意义和几何意义,用四元数表示的运动变量方程的计算更为简单,积分计算效率更高,而且其计算误差也能达到精度要求.