A Simple Lambert Algorithm
A Simple Lambert Algorithm
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DOI：
10.2514/1.36426
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发表时间：
2008-11
影响因子：
2.6
通讯作者：
G. Avanzini
中科院分区：
文献类型：
--
作者：
G. Avanzini
DOI：10.2514/1.36426开普勒运动框架中两点边值问题的经典结果允许导出通过空间中任意两点的轨道的新参数化。特别是，它表明，这些轨道可以明确地确定在垂直于弦连接的两个点的方向上的偏心率矢量分量。用横向偏心分量的参数化方法，可以有效地求解经典Lambert问题，即确定在给定时间内连接空间两点的轨道。虽然，从计算的角度来看，所得到的数值程序并没有提供优于优雅的巴廷的方法，其推导是相当少的要求从数学的角度和物理上更直观。标称a =半长轴c =弦e，e =偏心率和偏心率向量eF =沿弦沿着的偏心率分量eT =横向偏心率分量^ ic，^ ip，^ ih =弦、横向和法向单位向量p =半直弦或参数r，r
DOI: 10.2514/1.36426 A classic result for the two-point boundary value problem in the framework of Keplerian motion allows the derivation of a novel parametrization of orbits passing through two arbitrary points in space. In particular, it is shown that these orbits can be unambiguously identified in terms of their eccentricity vector component in the direction perpendicular to the chord connecting the two points. The parametrization, in terms of transverse eccentricitycomponent,lendsitselftoanefficientandintuitivesolutionalgorithmfortheclassicalLambertproblem, that is, the determination of the orbit that connects two points in space in a prescribed time. Although, from the computational point of view, the resulting numerical procedure does not provide advantages over the elegant Battin’s method, its derivation is considerably less demanding from the mathematical standpoint and physically more intuitive. Nomenclature a = semimajor axis c = chord e, e = eccentricity and eccentricity vector eF = eccentricity component along the chord eT = transverse eccentricity component ^ ic, ^ ip, ^ ih = chord, transverse, and normal unit vectors p = semilatus rectum or parameter r, r