论文标题
平均矢量元素中第三体扰动的非单明递归公式
Non-singular recursion formulas for third-body perturbations in mean vectorial elements
论文作者
论文摘要
在第三体扰动下对高度椭圆轨道的长期动力学的描述可能需要在一系列的半轴轴比率中扩展令人不安的功能，直到更高阶。为了避免在三角函数中处理长序列，我们将运动指向apsidal框架，并有效地消除了这种扩展的矢量形式的短期效应，直到任意顺序。然后，我们通过类似的矢量复发提供了开普勒运动的两个基本矢量的变化方程，它们没有奇异性，并采用一种对平均元素中流量的数值传播有用的紧凑形式。
The description of the long-term dynamics of highly elliptic orbits under third-body perturbations may require an expansion of the disturbing function in series of the semi-major axes ratio up to higher orders. To avoid dealing with long series in trigonometric functions, we refer the motion to the apsidal frame and efficiently remove the short-period effects of this expansion in vectorial form up to an arbitrary order. We then provide the variation equations of the two fundamental vectors of the Keplerian motion by analogous vectorial recurrences, which are free from singularities and take a compact form useful for the numerical propagation of the flow in mean elements.
