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首页> 外文期刊>Acta astronautica >Analytic expansions of luni-solar gravity perturbations along rotating axes for trajectory optimization—Part 2: The multipliers system and simulations
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Analytic expansions of luni-solar gravity perturbations along rotating axes for trajectory optimization—Part 2: The multipliers system and simulations

机译：轨迹优化的单太阳重力扰动沿旋转轴的解析扩展—第2部分：乘数系统和仿真

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摘要

An efficient self-contained trajectory optimization software is generated by making use of de Pontecoulant's analytic lunar theory removing the need for an outside third body ephemeris program to compute the lunar and solar position vectors at each integration step. The accelerations being further resolved along the rotating Euler-Hill frame after expansion to third order in the spacecraft radial distance, the adjoint differential equations are derived in a direct manner complementing the generation of the dynamic system of equations for full compatibility. Because the variation of parameters equations are cast in terms of the nonsingular equinoctial elements with the perturbation accelerations resolved in their analytic form along the rotating axes, the adjoint equations are also derived in the same manner providing a highly efficient and accurate system of equations for rapid computations in conjunction with Aerospace Corporation's NLP2 nonlinear programming codes to search for the initial values of the multipliers that steer the spacecraft towards its target orbit in minimum time. Numerical simulations show that the solutions obtained by the analysis developed in this paper are essentially identical to the more indirect approach based on the use of inertial accelerations obtained from a separate ephemeris generator and subsequent conversions to the thrust frame and equinoctial system.
机译：通过使用de Pontecoulant的解析月球理论来生成高效的独立轨迹优化软件，从而无需使用外部第三体星历程序来计算每个积分步骤中的月球和太阳位置矢量。在航天器径向距离上扩展到三阶之后，沿着旋转的Euler-Hill框架进一步分解加速度，以直接方式导出伴随的微分方程，从而补充了完全兼容的动力学方程组的生成。由于参数方程式的变化是根据非奇异的等容元进行的，其扰动加速度以解析形式沿旋转轴分解，因此也以相同的方式推导了伴随方程式，从而提供了一种高效，准确的方程组，可快速实现结合航空航天公司的NLP2非线性编程代码进行计算，以搜索乘数的初始值，该乘数将使航天器在最短的时间内指向目标轨道。数值模拟表明，本文分析得出的解基本上与更间接的方法相同，后者基于使用从单独的星历产生器获得的惯性加速度，并随后转换为推力架和等角线系统。

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