Periodic motion analysis around the libration points by polynomial expansion method in planar circular restricted three-body problem

We propose a polynomial expansion method to investigate periodic motions around both collinear and triangular libration points in the planar circular restricted three-body problem. The polynomial expansion method focuses on the approximate nonlinear polynomial relations between the two directions in...

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Bibliographic Details
Published in:Nonlinear dynamics 2018, Vol.91 (1), p.39-54
Main Authors: Qian, Ying-Jing, Yang, Xiao-Dong, Zhang, Wei, Zhai, Guan-Qiao
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Exact solutions
Lagrangian equilibrium points
Libration
Mechanical Engineering
Numerical analysis
Numerical methods
Original Paper
Polynomials
Three body problem
Vibration
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Summary:We propose a polynomial expansion method to investigate periodic motions around both collinear and triangular libration points in the planar circular restricted three-body problem. The polynomial expansion method focuses on the approximate nonlinear polynomial relations between the two directions in the motion plane, which provide an alternative way to inspect the periodic motions. Based on the nonlinear polynomial relations, the planar two-dimensional system is decoupled. As an example, the 3 rd order analytical solutions for the periodic motion are determined by solving the decoupled system. The efficiency of the polynomial expansion method has been validated by numerical method.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3818-1