Parametric stability analysis for planar bicircular restricted four-body problem

被引：15
作者：
Qian, Ying-Jing [1 ]
Yang, Lei-Yu [1 ]
Yang, Xiao-Dong [1 ]
Zhang, Wei [1 ]
机构：
[1] Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing,100124, China
来源：
Astrodynamics | 2018年 / 2卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Gravitation; -; Resonance; Stability;
D O I：
10.1007/s42064-017-0017-2
中图分类号：
学科分类号：
摘要：
Stability for the non-autonomous bicircular four-body model is analytically investigated in this study. The governing equation is derived from Newton’s law of gravity. When the distance between the infinitesimal mass and the third primary is expanded as Taylor expansions, the governing equation can be regarded as two parts: the unperturbed conservative system and the small periodically parametric excitations. The unperturbed system’s natural frequency and parametric frequency are analyzed for the possibility of principal parametric resonances. The method of multiple scales is applied directly to the governing equation. The stability conditions are obtained analytically for the principal parametric resonance. Numerical method demonstrates the efficiency of the analytical results. © Tsinghua University Press 2017.
引用
收藏
页码：147 / 159
页数：12
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