Anatomy of the Constant Radial Thrust Problem
Anatomy of the Constant Radial Thrust Problem
复制标题
恒定径向推力问题的剖析
DOI：
10.2514/2.4917
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发表时间：
2001
影响因子：
2.6
通讯作者：
R. Broucke
中科院分区：
文献类型：
--
作者：
M. Akella;R. Broucke
在本文中，我们打算研究一个众所周知的小推力问题，即恒定向外径向加速度问题的解流形，由于加速度始终在轨道平面内，因此轨道总是平面的。因此，我们把它当作一个两自由度问题，这个问题已知有一个封闭形式的解析解，因此，它的许多性质已经是明显的。1 i4解析解可以用标准的椭圆积分来表示，实际上并没有给出太多关于其基本性质的见解。为了更深入地了解这些性质，我们现在的研究将求助于经典力学和天体力学中通常使用的一些方法，例如由势函数施加的边界，以及问题的两个积分，能量和角动量。这些概念已经允许我们区分逃逸轨迹和有界轨迹。有效势的使用，以及能量常数的值，使我们能够确定禁止和允许的运动区域。请注意，有效势能的概念在类似的情况下已经被Prussing和Coverstone-Carroll [3]很好地使用过，但它们的初始条件仅限于圆形轨道。
N this paper, we intend to investigate the solution manifold for a fairly well knowlow-thrust problem,the constant outward radial acceleration.The trajectories are always planarbecause the acceleration is permanently in the plane of the orbit. Therefore, we treat it asatwo-degree-of-freedomproblem.Theproblemisknown tohave a closed-form analytical solution, and, therefore, a good number of its properties are already evident. 1i4 The analytical solution can be expressed in terms of the standard elliptic integrals that actually do not give too much insight into their basic properties. To gain more insight into these properties, our present investigation will have recourse to some methods that are usually employed in classical mechanics and celestial mechanics, such as the boundaries imposed by the potential function, as well as the two integrals of the problem, the energy and the angular momentum. These conceptsalready allowusto distinguish between the escape trajectories and the bounded trajectories. The use of the effective potential, as well as the value of the energy constant, allows us to dee ne forbidden, as well as allowable, regions of motion. Note that the concept of an effective potential energy has been well employed earlier by Prussing and Coverstone-Carroll 3 in a similar context, but their initial conditions are restricted to that of a circular orbit.