Abstract

The restricted elliptic doubly averaged three-body problem is considered. The terms up to the second order inclusive with respect to the orbital eccentricity of the perturbing body are retained in the expansion of the perturbing function. The elements of the elliptical orbit for the perturbed body are deemed arbitrary. The special, so-called linked orbits of a negligible-mass body are investigated by numerically integrating the averaged equations in Keplerian elements. For such orbits the points of their intersection with the orbital plane of the perturbing body are on different sides of this orbit. The evolution of hypothetical and some real cometary orbits is described in the simplest Sun-Jupiter-comet model; their differences from the corresponding orbits in the circular problem have been revealed.

中文翻译：

---

约束椭圆双平均三体问题中链接轨道的数值分析研究

摘要

考虑了受限椭圆双平均三体问题。关于摄动体的轨道偏心度直到二阶的术语（包括二阶）都保留在摄动功能的扩展中。被摄体的椭圆轨道的元素被认为是任意的。通过对开普勒元素中的平均方程进行数值积分，研究了可忽略质量体的特殊的所谓链接轨道。对于这样的轨道，它们与扰动体的轨道平面相交的点在该轨道的不同侧。在最简单的太阳木星彗星模型中描述了假设的和某些真实的彗星轨道的演化。揭示了它们与圆形问题中相应轨道的区别。