一种适用于大幅值Quasi周期轨道的数值构造方法  

A Numerical Construction Method for Large-amplitude Quasi Periodic Orbits

作　　者：李瑞龙 朱战霞[1] LI Ruilong;ZHU Zhanxia(School of Astronautics,Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]西北工业大学航天学院,西安710072

出　　处：《宇航学报》2023年第1期52-61,共10页Journal of Astronautics

基　　金：航天飞行动力学技术重点实验室基金(KGJ6142210210101)。

摘　　要：针对现有方法在构造大幅值quasi周期轨道时收敛性和通用性不足等问题,提出一种适用于大幅值quasi周期轨道的数值构造方法。首先针对2维不变环面的计算问题,设计了映射间隔约束的环面多步微分修正算法。在此基础上,采用自然参数延拓法和伪弧长延拓法两种不同的思路构造等映射间隔的quasi周期轨道族。接着以quasi-Vertical为对象分析了两种思路各自的特点。最后以quasi-Axial,quasi-DRO等为对象验证了方法对三角平动点及多对复特征值情况的适用性。仿真结果表明,所提出的方法能够简单有效地解决多种类型幅值比超过1.2的大幅值quasi周期轨道的数值计算问题。Aiming at the problems of convergence and generality of existing methods in constructing large-amplitude quasi periodic orbits,a suitable numerical construction method is proposed.Firstly,a multiple shooting torus correction algorithm with mapping interval constraint is designed to calculate the two-dimensional invariant torus.On this basis,two different ideas of natural parameter continuation and pseudo-arclength continuation are adopted to construct the quasi periodic orbital family with equal mapping time.Then,taking quasi-Vertical as the object,the characteristics of the two methods are analyzed.Finally,the applicability of the method to the triangular libration points and multiple pairs of complex eigenvalues is verified by constructing quasi-Axial and quasi-DRO,respectively.The numerical results show that the proposed method can easily and effectively solve the numerical problems of many types of quasi periodic orbits with large amplitude ratio over 1.2.

关 键 词：quasi周期轨道 不变环面 数值延拓 轨道设计 

分 类 号：V412.41[航空宇航科学与技术—航空宇航推进理论与工程]