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 dynamical model and a high-precision dynamical model. In response to 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. To address the issues where short-period orbits of triangular libration points are prone to divergence under the influence of perturbing forces, which is not conducive to engineering applications, and where the parallel shooting method has large computational loads and poor convergence when calculating multi-orbit short-period orbits, efficient calculation methods such as the optimized envelope area method and hybrid method for short-period orbits of triangular libration points under high-precision models are proposed. Using this method, an analysis of the short-period orbit at the lunar L4 point was conducted, revealing characteristics such as the envelope of short-period orbits in the lunar-Earth system under the high-precision model being approximately circular restricted three-body orbits but scattered within the envelope, and that 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