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Dynamic behavior analysis of tethered satellite system based on Floquet theory

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A Correction to this article was published on 16 May 2022

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Abstract

In this paper, an n-star general dynamic model of tethered satellite system with closed-loop configuration is provided. An analytical method for periodic solution stability of the general dynamic model is proposed based on Floquet theory, which proved that the periodic solution stability of the system depends on the maximum modulus for the eigenvalue of a matrix related to the Jacobian matrix. The periodic solution stability of a 3-star system with equilateral triangle as the initial configuration is analyzed as an example based upon the analytical method, and the results are verified by numerical simulation. The critical spin angular velocity caused by the tether mass and the parameter variation of the 3-star system is analyzed. The results show that the analytical method of periodic solution stability can solve the critical stable spin angular velocity of the tethered satellite system accurately, and the 3-star system can guarantee stable spin in the case of the spin angular velocity is higher than the critical spin angular velocity.

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Acknowledgements

The first and the third authors acknowledge the financial support from Natural Science Foundation of China (Key Project Grant No. 11732006), the fourth author acknowledges the financial support from Natural Science Foundation of China (Key Project Grant No. 91848205), and the other authors acknowledge the financial support from Natural Science Foundation of China (Grant No. 12072263, 11802235), Natural Science Foundation of Shaanxi Province (Grant No. 2020JQ-129), and State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures (Grant No. KF2020-26).

Funding

This work was supported by the Natural Science Foundation of China (Key Project Grant No. 11732006 and 91848205), Natural Science Foundation of China (Grant No. 12072263, 11802235), Natural Science Foundation of Shaanxi Province (Grant No. 2020JQ129), and State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures (Grant No. KF202026).

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Authors and Affiliations

  1. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, People’s Republic of China

    Guangnan Zhu & Qingjie Cao

  2. Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Kuan Lu & Kangyu Zhang

  3. School of Astronautics, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Panfeng Huang

  4. National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Panfeng Huang

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  1. Guangnan Zhu
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  2. Kuan Lu
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  3. Qingjie Cao
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  4. Panfeng Huang
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  5. Kangyu Zhang
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Correspondence to Kuan Lu.

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Zhu, G., Lu, K., Cao, Q. et al. Dynamic behavior analysis of tethered satellite system based on Floquet theory. Nonlinear Dyn 109, 1379–1396 (2022). https://doi.org/10.1007/s11071-022-07466-8

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  • DOI: https://doi.org/10.1007/s11071-022-07466-8

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