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Coupling dynamic characteristics of simplified model for tethered satellite system

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Abstract

The evolution of the attitude angle and the mechanical energy exchange between the bus system and the solar sail via the connecting wires are the main manifestations of the coupling dynamic effects on the orbit evolution, the attitude adjusting and the flexible vibration of the tethered satellite system. To investigate attitude evolution of the tethered system and the mechanical energy transfer/loss characteristics between the bus system and the solar sail via the connecting wires, a structure-preserving method is developed in this paper. Simplifying the tethered satellite system as a composite structure consisting of a particle and a flexible thin panel connected by four special springs, the dynamic model is deduced via the Hamiltonian variational principle firstly. Then, a structure-preserving approach that connects the symplectic Runge–Kutta method and the multi-symplectic method is developed. The excellent structure-preserving property of the numerical scheme constructed is presented to illustrate the credibility of the numerical results obtained by the constructed structure-preserving approach. From the numerical results on the mechanical energy transfer/loss in the composite structure, it can be found that the mechanical energy transfer tendency in the tethered system is dependent of the initial attitude angle of the system while the total mechanical energy loss of the system is almost independent of the initial attitude angle. In addition, the special stiffness range of the spring is found in the attitude angle evolution of the system, which provides a structural parameter design window for the connecting wires, that is, the duration needed to arrive the stable attitude is short when the stiffness of the wire is designed in this special range.

Graphic Abstract

The evolution of the attitude angle and the mechanical energy exchange between the bus system and the solar sail via the connecting wires are the main manifestations of the coupling dynamic effects on the orbit evolution, the attitude adjusting and the flexible vibration of the tethered satellite system. To investigate attitude evolution of the tethered system and the mechanical energy transfer/loss characteristics between the bus system and the solar sail via the connecting wires, a structure-preserving method is developed in this paper. Simplifying the tethered satellite system as a composite structure consisting of a particle and a flexible thin panel connected by four special springs, the dynamic model is deduced via the Hamiltonian variational principle firstly. Then, a structure-preserving approach that connects the symplectic Runge-Kutta method and the multi-symplectic method is developed. The excellent structure-preserving property of the numerical scheme constructed is presented to illustrate the credibility of the numerical results obtained by the constructed structure-preserving approach. From the numerical results on the mechanical energy transfer/loss in the composite structure, it can be found that the mechanical energy transfer tendency in the tethered system is dependent of the initial attitude angle of the system while the total mechanical energy loss of the system is almost independent of the initial attitude angle. In addition, the special stiffness range of the spring is found in the attitude angle evolution of the system, which provides a structural parameter design window for the connecting wires, that is, the duration needed to arrive the stable attitude is short when the stiffness of the wire is designed in this special range.

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Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grants 11972284 and 11872303), the Fund for Distinguished Young Scholars of Shaanxi Province (2019JC-29), the Fund of the Youth Innovation Team of Shaanxi Universities, and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (Grant GZ19103). The authors declare that they have no conflict of interest with the present manuscript.

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Authors and Affiliations

  1. School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an, 710048, China

    Weipeng Hu, Yulu Huai & Mengbo Xu

  2. State Key Laboratory of Eco-Hydraulics in Northwest Arid Region of China, Xi’an University of Technology, Xi’an, 710048, China

    Weipeng Hu

  3. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, China

    Zichen Deng

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  1. Weipeng Hu
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Correspondence to Weipeng Hu.

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Hu, W., Huai, Y., Xu, M. et al. Coupling dynamic characteristics of simplified model for tethered satellite system. Acta Mech. Sin. 37, 1245–1254 (2021). https://doi.org/10.1007/s10409-021-01108-9

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