一种改进的相对轨道动力学模型

线性化的Clohessey-Whiltshire(C-W)方程描述相对运动虽然方便,但是精度不高,为了解决这一问题,提出了一种C-W方程的改进形式。首先基于C-W方程的推导,分析了在对中心引力取近似的过程中导致原方程不准确的数学原因和物理现象;然后通过对简化部分的数量级进行分析和比较,将原推导过程中忽略掉的部分重要内容重新予以考虑,并运用数学变换将新加入的内容合并转化,最终给出了一组非齐次线性常系数微分方程,在不增加计算复杂度的情况下提高了精度。仿真验证表明该方程在圆轨道下相对于C-W方程精度改善很多,小椭圆轨道下也消除了C-W方程的长期误差。

An Improved Form of Relative Trajectories Dynamics Model

The linearized C-W equation is used very expediently, but it has the problem of inaccuracy. An improved equation based on C-W equation was presented, which can describe the formation flying more accurate. Firstly, the derivative process of C-W equation was analyzed and the inaccurate reason was find out. Then parts of contents were adding and re-derivation, which has been ignored in order to simplify the equation in the original derivative process. And lots of mathematical transformations were used to reduce the new equation. Finally, a set of linear differential equations with constant coefficients was given, which can improving the precision without increasing the complexity. Simulation shows that in the condition of circular orbit, the accuracy was improved a lot comparing with the C-W equation, while in nearly circular orbit, the long-term error of C-W equation was eliminated.