Comparison of Two Methods in Satellite Formation Flying
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摘要: 目前卫星编队飞行动力学与控制的研究得到了广泛的重视,这些研究的理论主要是基于描述卫星相对运动的Clohessy-Wiltshire(C-W)方程。但根据特例及定性分析,表明C-W方程在初始条件的选取、解的周期性等方面与实际情况不符,从星的能量也不守恒。以卫星轨道根数为基础,提出了卫星编队飞行中的相对轨道根数法,克服了C-W方程的局限性,物理概念清楚,应用范围广,解的周期性成为自然结论。在主星为小偏心率的情况下,得到了简化的相对运动方程。最后对两种方法进行了比较,指出了C-W方程的局限性及其原因。Abstract: Recently,the research of dynamics and control of the satellite formation flying has been attracting a great deal of attentions of the researchers.The theory of the research was mainly based on Clohessy-Wiltshire's(C-W's) equations,which describe the relative motion between two satellites.But according to some special examples and qualitative analysis,neither the initial parameters nor the period of the solution of C-W's equations accord with the actual situation,and the conservation of energy is no longer held.Anew method developed from orbital element description of single satellite,named relative orbital element method(ROEM),was introduced.This new method,with clear physics conception and wide application range,overcomes the limitation of C-W's equation,and the periodic solution is a natural conclusion.The simplified equation of the relative motion is obtained when the eccentricity of the main satellite is small.Finally,the results of the two methods(C-W's equation and ROEM) are compared and the limitations of C-W's equations are pointed out and explained.
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