论文标题
使用平均理论在小加速度下用于扰动开普勒运动的分析解决方案
Analytic Solution for Perturbed Keplerian Motion Under Small Acceleration Using Averaging Theory
论文作者
论文摘要
开发了一种新的方法，用于基于渐近膨胀的小扰动加速度的分析轨道繁殖。该方法通过利用线性系统和平均理论来改善现有的一阶渐近扩展。该溶液始于高斯行星方程相对于小扰动和六轨道元件的线性化。然后，根据世俗和短期成分获得近似解决方案。该方法是在由恒定切向加速度扰动的开普勒轨道组成的低伪装机动场景上测试的，可以根据椭圆形积分来获得解决方案。结果表明，相对于最先进的方法，位置传播误差约为一个数量级。除病理情况外，LEO轨道的位置精度通常在数十米的范围内，在5个轨道周期传播后无量纲的切向加速度为1E-5。
A novel approach is developed for analytic orbit propagation based on asymptotic expansion with respect to a small perturbative acceleration. The method improves upon existing first order asymptotic expansions by leveraging on linear systems and averaging theories. The solution starts with the linearization of Gauss planetary equations with respect to both the small perturbation and the six orbital elements. Then, an approximate solution is obtained in terms of secular and short period components. The method is tested on a low-thrust maneuver scenario consisting of a Keplerian orbit perturbed by a constant tangential acceleration, for which a solution can be obtained in terms of elliptic integrals. Results show that the positional propagation error is about one order of magnitude smaller with respect to state-of-the-art methods. The position accuracy for a LEO orbit, apart from pathological cases, is typically in the range of tens of meters for a dimensionless tangential acceleration of 1e-5 after 5 orbital periods propagation.
