Relative Motion and the Geometry of Formations in Keplerian Elliptic Orbits with Arbitrary Eccentricity
Relative Motion and the Geometry of Formations in Keplerian Elliptic Orbits with Arbitrary Eccentricity
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DOI：
10.2514/1.25941
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发表时间：
2007-07
影响因子：
2.6
通讯作者：
P. Sengupta;S. Vadali
中科院分区：
文献类型：
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作者：
P. Sengupta;S. Vadali
用于设计编队飞行相对轨道的著名 Hill-Clohessy-Wiltshire 方程基于圆形参考轨道。诸如投影圆形或一般圆形相对轨道之类的经典解在存在偏心率的情况下不再有效。本文研究偏心率对开普勒轨道相对运动的影响。推导了相对位置坐标中有界运动的新线性条件，该条件对于参考轨道的任意偏心率和历元都有效。结果表明，用于椭圆轨道交会的 Tschauner-Hempel 方程的解与使用小轨道单元差异描述相对运动直接相关。还开发了一种有意义的几何参数化，用于任意偏心率的开普勒椭圆轨道附近的相对运动。研究并利用偏心率引起的效应以获得所需的相对轨道形状。还导出了将这些参数与初始条件以及微分经典和非奇异元素相关的方程。这种参数化对于分析更复杂的模型非常有用，例如非线性相对运动问题。
The well-known Hill-Clohessy-Wiltshire equations that are used for the design of formation flight relative orbits are based on a circular reference orbit Classical solutions such as the projected circular or general circular relative orbit are no longer valid in the presence of eccentricity. This paper studies the effects of eccentricity on relative motion for Keplerian orbits. A new linear condition for bounded motion in relative position coordinates is derived that is valid for arbitrary eccentricities and epoch of the reference orbit. It is shown that the solutions to the Tschauner-Hempel equations that are used for rendezvous in elliptic orbits are directly related to the description of relative motion using small orbital element differences. A meaningful geometric parameterization for relative motion near a Keplerian elliptic orbit of arbitrary eccentricity is also developed. The eccentricity-induced effects are studied and exploited to obtain desired shapes of the relative orbit. Equations relating these parameters to initial conditions and differential classical and nonsingular elements are also derived. This parameterization is very useful for the analysis of more complicated models, such as the nonlinear relative motion problem.