一种适用于大幅值 Quasi 周期轨道的数值构造方法

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-arelength 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.