DEPLOYMENT OF THE ROTATING TWO BODIES TETHER IN AN ORBIT

• Дата: 2026
• Автори: WANG, Ch., ZAKRZHEVSKYI, O. E.
• Формат: Стаття
• Опубліковано: текст 3 2026
• Онлайн доступ: https://journal-itm.dp.ua/ojs/index.php/ITM_j1/article/view/188
• Назва журналу: Technical Mechanics

The focus of the study is a compact orbital tether consisting of two bodies that must be deployed from a spacecraft so that after deployment it rotates at a constant angular speed and attains a prescribed length. The end masses are taken as equal, and the connecting cable is assumed massless. The aim of the research is to develop a feedforward control for the tether length, taking into account the gravitational torque exerted by the central Newtonian field of forces. Initial rotation of the tether about the orbit’s binormal is employed for deployment. The research consists of two stages. The development of the control law is based on the tether length in the first stage, which provides the performance of the desired deployment. The tether motion equations, expressed in spherical polar coordinates for a particular case of tether motion in the orbital plane, are used at this stage. In the second investigative phase, a numerical simulation of the deployment dynamics of a tether under the effect of the developed feedforward control law is performed using the tether length. As a mathematical model of the tether, the full set of motion equations for a variable‑length tether in spherical polar coordinates is employed, describing the spatial motion of bodies. The tensile force of the cable entering these equations is described by the control law governing length variation and its first two time derivatives. The novelty of this study lies in devising a feedforward control law that treats the tether as an underactuated mechanical system. Analytical mechanics, numerical techniques, and authors‑developed methods were employed in this research. The results enable determination of the permissible ranges of deployment parameters, facilitating this type of deployment. Practically, the findings allow small tethers to be deployed in orbit and brought to uniform rotation at a specified length via tether length control. REFERENCES 1. Alpatov A. P., Beletsky V. V., Dranovskii V. I., Khoroshilov V. S. et al. Dynamics of Tethered Space Systems. Advances in Engineering. Boca Raton: CRC Press, 2010. 223 pp. 2. Alpatov A. P., Zakrzhevskii A. E. Passive deployment of a tether between two bodies in orbit. International Applied Mechanics. 1999. V. 35. No.10. Pp. 1053-1058. https://doi.org/10.1007/BF02682318 3. Beletsky V. V. Motion of an artificial satellite about its center of mass. Jerusalem: Israel Program for Scientific Translations. 1966. 4. Beletsky V. V., Levin E. M. Dynamics of Space Tether Systems. V. 83. Advances in the Astronautical Sciences, San Diego: Univelt, 1993. 499 pp. 5. Huang P., Zhang F., Chen L. et al. A review of space tether in new applications. Nonlinear Dynam. 2018. V. 94. Pp. 1-19. 6. Kang J., Zhu Z., Santaguida L. F. Analytical and experimental investigation of stabilizing rotating uncooperative target by tethered space tug. IEEE Trans. Aero. Electron. Syst. 2021. V. 57. No. 4. Pp. 2426-2437. https://doi.org/10.1109/TAES.2021.3061798 7. Li Z., Meng Z., Huang P. Spin-up control of tethered space station for artificial gravity task. IEEE International Conference on Robotics and Biomimetics (ROBIO). 2019. Pp. 2502-2508.https://doi.org/10.1109/ROBIO49542.2019.8961375 8. Rajkumar A., Bannova O. A three-body spacecraft as a testbed for artificially-induced gravity research in low earth orbit. 2020. ARC AIAA. 2020-4110. https://doi.org/10.2514/6.2020-4110 9. Trushlyakov V.I., Yudintsev V.V. Rotary space tether system for active debris removal. J. Guid. Control Dynam. 2020. V. 43. No. 2. Pp. 354-364. https://doi.org/10.2514/1.G004615 10. Wang Ch., Zakrzhevskiy O. E. Deployment of the space tether in the centrifugal force field with alignment to the local vertical. Teh. Meh. 2024. No.1. Pp. 26-39. https://doi.org/10.15407/itm2024.01.026 11. Zakrzhevskii A. E. Method of deployment of a space tethered system aligned to the local vertical. J. of Astronaut. Sci. 2016. V. 63. Pp. 221-236. https://doi.org/10.1007/s40295-016-0087-z