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首页> 外文期刊>Journal of guidance, control, and dynamics >Analytic Theory for High-Inclination Orbits in the Restricted Three-Body Problem
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Analytic Theory for High-Inclination Orbits in the Restricted Three-Body Problem

机译：约束三体问题中高倾角轨道的解析理论

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This paper explores the analytical solution properties surrounding a hypothetical orbit in an invariant plane perpendicular to the line joining the two primaries in the circular restricted three-body problem. Assuming motion can be maintained in the plane, Jacobi's integral equation can be analytically integrated, yielding a closed-form expression for the period and path of the third body expressed with elliptic integral and elliptic function theory. In this case, the third body traverses a circular path with nonuniform speed. In a strict sense, the in-plane assumption cannot be maintained naturally. However, the hypothetical orbit is shown to satisfy Jacobi's integral equation and the tangential motion equation exactly and the other two motion equations approximately in bounded-averaged and banded sense. More important, the hypothetical solution can be used as the basis for an iterative analytical solution procedure for the three-dimensional trajectory where corrections are computable in closed form. In addition, the in-plane assumption can be strictly enforced with the application of a modulated thrust acceleration which is expressible in closed form. Presented methodology is primarily concentrated on halo-class orbits.
机译：本文探讨了在与圆形受限三体问题中的两个原边相连的线垂直的不变平面内的假设轨道周围的解析解性质。假设可以在平面上保持运动，则可以对Jacobi积分方程进行解析积分，从而用椭圆积分和椭圆函数理论得出第三体的周期和路径的封闭形式。在这种情况下，第三物体以不均匀的速度横越圆形路径。从严格意义上讲，平面内假设无法自然维持。但是，假设的轨道显示为完全满足Jacobi积分方程和切向运动方程，并且其他两个运动方程近似在有界平均和带状意义上满足。更重要的是，假设的解可以用作三维轨迹的迭代解析解程序的基础，在该三维轨迹中，校正可以封闭形式进行计算。另外，可以通过以封闭形式表示的调制推力加速度来严格执行平面内假设。提出的方法主要集中在晕圈轨道上。

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