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Two-Body Orbital Boundary Value Problems in Regularized Coordinates
The Journal of the Astronautical Sciences ( IF 1.8 ) Pub Date : 2019-12-20 , DOI: 10.1007/s40295-019-00204-0
Bharat Mahajan , Srinivas R. Vadali

Lambert’s two-body orbital boundary value problem (BVP) is the determination of the terminal velocity vectors of a trajectory connecting two fixed positions in a specified transfer time. The solution to Lambert’s problem is often the basis for preliminary trajectory design and optimization. In this work, several related two-body orbital BVPs, with constraints involving terminal velocities, flight-path angle, Δv, final radius, transfer angle, etc., are studied. Exact solutions to these BVPs are derived in a universal form via the Kustaanheimo-Stiefel transformation. The solutions are regular and completely analytic if the energy of the transfer orbit is known a priori. Otherwise, they require root-finding of either a polynomial or a transcendental equation with well-defined bounds on its roots. The algorithms developed are validated on several orbit transfer problems and can enable complex mission analysis and parametric studies or serve as initial guesses for high-fidelity numerical optimization schemes.

中文翻译:

正则坐标系中的两体轨道边值问题

兰伯特的两体轨道边界值问题(BVP)是确定在指定的传递时间内连接两个固定位置的轨迹的最终速度矢量。兰伯特问题的解决方案通常是初步轨迹设计和优化的基础。在这项工作中,多个相关的两体轨道边值问题,与涉及终端速度的限制,飞行路径角,Δ v,最终半径,传递角等。通过Kustaan​​heimo-Stiefel变换以通用形式导出了这些BVP的精确解。如果转移轨道的能量是先验已知的,则解决方案是规则的并且是完全解析的。否则,他们需要对根部有明确定义的多项式或超越方程式求根。所开发的算法在几个轨道转移问题上得到了验证,可以进行复杂的任务分析和参数研究,或者用作高保真数值优化方案的初步猜测。
更新日期:2019-12-20
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