Existence and stability of periodic oscillations of a rigid dumbbell satellite around its center of mass

Jifeng Chu; Zaitao Liang; Pedro J. Torres; Zhe Zhou

doi:10.3934/dcdsb.2017130

Article Contents

2017, Volume 22, Issue 7: 2669-2685. Doi: 10.3934/dcdsb.2017130

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Existence and stability of periodic oscillations of a rigid dumbbell satellite around its center of mass

1.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2.
Department of Mathematics, College of Science, Hohai University, Nanjing 210098, China
3.
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
4.
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Author Bio: E-mail address: jifengchu@126.com (J. Chu); E-mail address: liangzaitao@sina.cn(Z. Liang); E-mail address: ptorres@ugr.es (P. J. Torres); E-mail address: zzhou@amss.ac.cn (Z. Zhou)
* Corresponding author: Jifeng Chu
* Corresponding author: Jifeng Chu

Received: July 2016

Revised: November 2016

Published: October 2017

Jifeng Chu was supported by the National Natural Science Foundation of China (Grant No. 11171090 and No. 11671118). Zaitao Liang was supported by the Fundamental Research Funds for the Central Universities (Grant No. KYZZ15−0155). Pedro Torres was partially supported by Spanish MICINN Grant with FEDER funds MTM2014-52232-P. Zhe Zhou was supported by the National Natural Science Foundation of China (Grant No. 11301512) and the Key Lab of Random Complex Structures and Data Science, Chinese Academy of Sciences (Grant No. 2008DP173182).

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Abstract

We study the existence and stability of periodic solutions of a differential equation that models the planar oscillations of a satellite in an elliptic orbit around its center of mass. The proof is based on a suitable version of Poincaré-Birkhoff theorem and the third order approximation method.

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Mathematics Subject Classification: Primary:34C25.

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Figure 1. The region of stability $\Delta$

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References

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