Planar periodic orbits’ construction around libration points with invariant manifold technique

This paper revisits the planar periodic motions around libration points in circular restricted three-body problem based on invariant manifold technique. The invariant manifold technique is applied to construct the nonlinear polynomial relations between ξ-direction and η-direction of a small celestia...

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Bibliographic Details
Published in:Proceedings of the Institution of Mechanical Engineers. Part G, Journal of aerospace engineering Journal of aerospace engineering, 2019-02, Vol.233 (2), p.498-509
Main Authors: Qian, Ying-Jing, Yang, Xiao-Dong, Zhai, Guan-Qiao, Zhang, Wei
Format: Article
Language:English
Subjects:
Celestial mechanics
Computer simulation
Construction planning
Invariants
Lagrangian equilibrium points
Libration
Manifolds (mathematics)
Nonlinear analysis
Orbits
Polynomials
Terminal constraints
Three body problem
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Summary:This paper revisits the planar periodic motions around libration points in circular restricted three-body problem based on invariant manifold technique. The invariant manifold technique is applied to construct the nonlinear polynomial relations between ξ-direction and η-direction of a small celestial body during its periodic motion. Such direct nonlinear relations reduce the dimension of the dynamical system and facilitate convenient approximate analytical solutions. The nonlinear directional relations also provide terminal constraints for computing periodic motions. The method to construst periodic orbits proposed in this study presents a new point of view to explore the orbital dynamics. As an application in numerical simulations, nonlinear relations are adopted as topological terminal constraints to construct the periodic orbits with differential correction procedure. Numerical examples verify the validity of the proposed method for both collinear and triangular libration cases.
ISSN:0954-4100
2041-3025
DOI:10.1177/0954410017736544