Dynamics and Staged Deployment Strategy for a Spinning Tethered Satellite System
Abstract
1. Introduction
2. Dynamic Modeling of the STSS
2.1. System Description
2.2. Dynamic Modeling of the Flexible Variable-Length Tether Element
2.3. Governing Equations of the Constrained Tether Multibody System
3. Staged Deployment Strategy
3.1. First Stage of Deployment
3.2. Second Stage of Deployment
4. Simulation and Analysis
4.1. Dynamic Model Validation
4.2. Single Sub-Satellite Configuration Without Space Environmental Forces
4.3. Single Sub-Satellite Configuration with an Improved Staged Deployment Strategy
4.4. Twin Sub-Satellite Configuration Considering Space Environmental Forces
5. Conclusions
- (1)
- A multibody dynamic model is developed to analyze the nonlinear characteristics of the STSS deployment process, employing the ANCF within an ALE framework in conjunction with Lagrange multipliers. This model effectively captures the flexibility and length variation of the tether, as well as the attitude of the satellites. Both the gravitational gradient force and the Coriolis force are taken into account. Unlike the traditional massless/rigid rod model, the tether in this model is discretized into multiple flexible elements, accounting for both axial and bending deformations, thereby significantly enhancing the accuracy in characterizing the tether’s behavior.
- (2)
- A staged deployment control strategy based on safety tension division is proposed to address the problem of mutual restriction between high-speed spin and tether tension in the STSS. In the first stage, a high spinning angular velocity of the central spacecraft and the deployment velocity of the tether are planned to ensure deployment efficiency, and meanwhile eliminating the libration angle and oscillations in the STSS. Moreover, a method for calculating maximum tether tension is proposed to divide the deployment stage. When the tether tension exceeds the maximum critical value, the deployment enters the second stage. In this stage, the tether tension can be gradually reduced with the decrease of the spinning angular velocity of the STSS, which ensures the safety of the deployment process.
- (3)
- Simulation results indicate that, when considering flexibility, the STSS exhibits greater oscillations in dynamic responses, such as libration angle and tether tension. Therefore, the application of the flexible model is essential to accurately reflect the vibration characteristics and dynamic behavior of the STSS. The accuracy of the dynamic model and the effectiveness of the proposed staged deployment strategy are demonstrated by numerical simulations, and torque compensation and deployment velocity transitions are introduced to mitigate libration angle fluctuations, thereby optimizing the dynamic performance of the STSS during deployment. Furthermore, the analysis of deployment dynamics under space environmental forces reveals that, while the STSS in vertical-to-ground orientation remains stable, the STSS in parallel-to-ground orientation experiences significant instabilities, reflected in fluctuations of the libration angle, out-of-plane angle, and attitude of the satellites. These instabilities can be effectively mitigated through space force compensation.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameters | Value | Units |
---|---|---|
Principal inertia of central spacecraft | (200, 200, 200) | kg·m2 |
Principal inertia of sub-satellite | (0.02, 0.02, 0.02) | kg·m2 |
Mass of central spacecraft | 1500 | kg |
Mass of sub-satellite | 5 | kg |
Radius of central spacecraft | 0.5 | m |
Linear density of tether | 0.02607 | kg/m |
Diameter of tether | 2 | mm |
Elastic modulus of tether | 128 | GPa |
Tensile strength of tether | 827 | MPa |
Total tether length | 800 | m |
Threshold length of tether element | 50 | m |
Initial spinning angular velocity | 1 | rad/s |
Initial libration angle | π/6 | rad |
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Zhang, Y.; Chen, K.; Guo, J.; Wei, C. Dynamics and Staged Deployment Strategy for a Spinning Tethered Satellite System. Aerospace 2025, 12, 611. https://doi.org/10.3390/aerospace12070611
Zhang Y, Chen K, Guo J, Wei C. Dynamics and Staged Deployment Strategy for a Spinning Tethered Satellite System. Aerospace. 2025; 12(7):611. https://doi.org/10.3390/aerospace12070611
Chicago/Turabian StyleZhang, Yue, Kai Chen, Jiawen Guo, and Cheng Wei. 2025. "Dynamics and Staged Deployment Strategy for a Spinning Tethered Satellite System" Aerospace 12, no. 7: 611. https://doi.org/10.3390/aerospace12070611
APA StyleZhang, Y., Chen, K., Guo, J., & Wei, C. (2025). Dynamics and Staged Deployment Strategy for a Spinning Tethered Satellite System. Aerospace, 12(7), 611. https://doi.org/10.3390/aerospace12070611