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首页> 外文期刊>The Journal of the Astronautical Sciences >The Streamlined and Complete Set of the Nonsingular J2-Perturbed Dynamic and Adjoint Equations for Trajectory Optimization in Terms of Eccentric Longitude
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The Streamlined and Complete Set of the Nonsingular J2-Perturbed Dynamic and Adjoint Equations for Trajectory Optimization in Terms of Eccentric Longitude

机译：偏心经度的轨迹优化的非奇异J2摄动动力学和伴随方程的简化且完整的集合

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摘要

The complete set of the dynamic and multipliers differential equations for a nonsingular set of equinoctial elements where the eccentric longitude stands for the sixth or fast orbital element are derived in a more straightforward and streamlined manner as compared to a previous derivation also presented by this author. The mathematics are validated through comparison with the original formulation as well as with two other formulations using the mean longitude and the true longitude elements as the respective sixth element of the equinoctial set. Furthermore, this new formulation is used to derive the costate or adjoint differential equations by fully accounting for the secular first-order perturbative effect of the second zonal harmonic J2, and the complete set of the perturbed dynamic and adjoint system of equations are also validated by direct comparison with the two previously derived formulations using the mean and true longitudes respectively The present formulation as well as the one using the true longitude as the sixth orbital element remove the need to solve Kepler's transcendental equation at each integration step, a need that is inevitable when the mean longitude formulation is used, because in the latter case the right-hand sides of the various differential equations cannot be written directly in terms of the mean longitude. The inclusion of the ,/3 and JA terms can be similarly accounted for with both the eccentric and true longitude sets and mutually validated also. This particular formulation has been adopted by several aerospace contractors in the United States to build specialized flight guidance software to steer payloads released in high energy orbits to their final destinations using highly efficient low-thrust propulsion.
机译：与该作者先前提出的推导方法相比，以更直接，更精简的方式推导了一组非奇异的等要素线动力学和乘子微分方程组，其中偏心经度代表第六或快速轨道元素。通过与原始公式以及使用平均经度和真实经度元素作为等均线集的第六个元素的两个其他公式进行比较来验证数学。此外，该新公式可通过充分考虑二次区域谐波J2的长期一阶微扰效应来推导肋式或伴随微分方程，并且通过以下方式验证了方程组的扰动和伴随系统的完整集合：与分别使用均值和真实经度的两个先前推导公式的直接比较本公式以及使用真实经度作为第六个轨道元素的公式消除了在每个积分步骤中求解开普勒先验方程的需要，这是不可避免的当使用平均经度公式时，因为在后一种情况下，各种微分方程的右侧无法直接根据平均经度来写。 ，/ 3和JA术语的包含可以类似地用偏心经度和真实经度集来说明，并且也可以相互验证。美国的几个航空承包商都采用了这种特殊的配方，以构建专门的飞行指导软件，以利用高效的低推力推进将高能轨道中释放的有效载荷引向最终目的地。

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