关键词: 圆型限制性三体问题, 三角平动点, 坐标延拓, 包络面积, 短周期轨道

Abstract:

This paper first establishes the circular restricted three-body dynamics model and a high-precision dynamical model. To address the limited orbital extension capability along the x direction， an angle extension method for short-period orbits of triangular libration points is proposed， which solves the family of larger-range lunar-Earth triangular libration points’ short-period orbits. Considering that short-period orbits around the triangular libration points are prone to divergence under the influence of perturbing forces， thereby limiting their engineering applications， and that the parallel shooting method has large computational loads and poor convergence when calculating multi-orbit short-period orbits， this study proposes efficient calculation methods under high-precision models， including the optimized envelope area method and hybrid method for short-period orbits of triangular libration points. Using the proposed methods， an analysis of the short-period orbit at the lunar L4 point was conducted. The results indicate that under the high-precision model， the envelope of short-period orbits in the lunar-Earth system is approximately consistent with that of circular restricted three-body problem， while orbits are scattered within the envelope. Moreover， short-period orbits calculated at different epochs ultimately stabilize within a certain range. These findings lay the foundation for the practical application of triangular libration points.

Key words: circular restricted three-body problem, triangular translation point, coordinate continuation, envelope area, short-periodic orbit