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The dynamic instability analysis of electrodynamic tether system

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Abstract

The libration motion of conductive tether in the electrodynamic tether system has been demonstrated to be inherently unstable. However, the relationship between the instability of libration motion and the tether current, orbital inclination and attitude of libration motion has not been thoroughly investigated. The novelty of this paper lies in the determination of the critical ranges of attitude and \(\varepsilon\) that lead to rapid tumbling of libration motion, and the study of how the instability of libration motion varies with attitude and \(\varepsilon\), where \(\varepsilon\) accounts for the effects of tether current and orbital inclination. Some numerical simulations were conducted to demonstrate that, as attitude and \(\varepsilon\) increase, the instability of libration motion gradually becomes more pronounced, especially when the attitude angle or \(\varepsilon\) exceeds the respective critical range, in which case the libration will become unstable even with implementation of control strategy. The critical range of tether current, which leads to rapid tumbling of the libration motion, can be determined based on the range of \(\varepsilon\), and this range of current can serve as a basis for designing the current regulation range, thereby preventing rapid tumbling that may result from improperly designed or regulated current values. The critical range of attitude angle can be utilized to monitor attitude motion and to avoid quick tumbling caused by excessive attitude angle.

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Data availability

The datasets supporting the conclusions of this article are included within the article. The datasets are available from the corresponding author on reasonable request.

Abbreviations

EDT:

Electrodynamic tether

TDAS:

Time-delayed autosynchronization

ETDA:

Extended time-delayed autosynchronization

m m :

Mass of main satellite

m s :

Mass of sub-satellite

m t :

Mass of tether

L :

Length of tether

\(F_{I} \left( {OXYZ} \right)\) :

Global inertial frame

\(F_{o} \left( {o_{m} x_{o} y_{o} z_{o} } \right)\) :

Orbital frame of main satellite

\(\theta\) :

In-plane angle of tether

\(\phi\) :

Out-of-plane angle of tether

\(I_{m}\) :

Tether current

\(\mu_{m}\) :

Geomagnetic dipole moment

\(i_{o}\) :

Orbital inclination

\(\mu_{g}\) :

Gravitational constant

\(Q_{\theta } ,\;Q_{\phi }\) :

Control input with respect to in-plane and out-of-plane angles

\(\Omega\) :

Orbital angular velocity

v :

Argument of latitude

t :

Time

\(I_{c}\) :

Control current

\(k_{\theta } ,\;k_{\phi }\) :

Feedback gains

\(R_{\theta } ,\;R_{\phi }\) :

Memory parameters

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Funding

This work was supported by the National level project (Grant No. KISP2020010301), National Natural Science Foundation of China (Grant No. 12102038) and National level project (Grant No. 2022YFB3902702).

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Authors and Affiliations

  1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Xialin Li, Keying Yang & Jingrui Zhang

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  1. Xialin Li
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Correspondence to Keying Yang.

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Li, X., Yang, K. & Zhang, J. The dynamic instability analysis of electrodynamic tether system. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09771-w

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