High-order state transition polynomial with time expansion based on differential algebra
High-order state transition polynomial with time expansion based on differential algebra
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DOI：
10.1016/j.actaastro.2019.03.068
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发表时间：
2019-10
影响因子：
3.5
通讯作者：
Zhen-Jiang Sun;P. Di Lizia;F. Bernelli-Zazzera;Ya-zhong Luo;Kun-Peng Lin
中科院分区：
文献类型：
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作者：
Zhen-Jiang Sun;P. Di Lizia;F. Bernelli-Zazzera;Ya-zhong Luo;Kun-Peng Lin
在这项研究中，基于微分代数(DA)技术，发展了一种带时间扩展的高阶状态转移多项式(STP-T)方法，用于将初始轨道状态围绕其参考值传播到可变的结束时间。STP-T是围绕参考初态和参考传播时间展开的最终轨道状态的高阶泰勒多项式。由于最终状态对于初始状态和传播时间的不同分量通常表现出不同的非线性，因此将加权阶格式与STP-T相结合，使得STP-T在具有较高非线性的分量上具有较高的阶数，而在具有较低非线性的分量上具有较低的阶数。然后，提出了一种误差估计方法，该方法可以先验地提供STP-T的误差分布，对于选择合适的阶数和确定相应的有效位移范围是有用的。最后，对STP-T方法在三种典型轨道动力学下的轨道传播进行了测试：未摄动的开普勒体动力学、J2摄动的二体动力学和非线性相对动力学。数值模拟结果表明，在一定的初始状态和传播时间的有效范围内，STP-T能很好地逼近最终状态，先验估计误差在趋势和幅度上接近精确误差，并且在不损失精度的情况下，加权阶格式可以显著节省计算量。
In this study, a high-order state transition polynomial with time expansion (STP-T) method is developed to propagate an initial orbital state around its reference value to a variable final time based on the differential algebra (DA) technique. STP-T is a high-order Taylor polynomial of the final orbital state expanded around the reference initial state and reference propagation time. Since the final state usually shows different nonlinearity with respect to different components of initial state and propagation time, a weighted-order scheme is combined with STP-T, which enables the STP-T to have higher orders on the components with higher nonlinearity and lower orders on the components with lower nonlinearity. Then, an error estimation method is presented, which can a priori provide the error profiles of a STP-T and is useful for selecting a proper order and determining the corresponding valid ranges of displacements. Finally, the STP-T method is tested for orbit propagation under three typical orbital dynamics: the unperturbed Keplerian dynamics, the J 2 perturbed two-body dynamics, and the nonlinear relative dynamics. The numerical simulation results indicate that the STP-T supplies a good approximation of the final state within certain valid ranges of initial state and propagation time, the a priori estimated error is close to the exact error in sense of trend and magnitude, and the computational cost can be significantly saved by the weighted-order scheme without loss of accuracy.