Studying the CubeSat 6U nanosatellites uncontrolled motion relative to the center of mass under the influence of aerodynamic and gravitational moments

Article

Published: 27.01.2025

Authors: Barinova E.V., Belokonov I.V., Timbai I.А.

Published in issue: #1(157)/2025

DOI: 10.18698/2308-6033-2025-1-2419

Category: Aviation and Rocket-Space Engineering | Chapter: Aircraft Dynamics, Ballistics, Motion Control

The paper presents results of studying the CubeSat 6U nanosatellites passive motion dynamics relative to the center of mass taking into account features of the mathematical model of the aerodynamic frontal drag force when moving in a low circular orbit. A system of equations is obtained to determine the nanosatellite equilibrium positions in the orbital coordinate system exposed to aerodynamic and gravitational moments. For a special case of the center of mass displacement from the nanosatellite geometric center along the longitudinal axis, an analytical solution to this system of equations is found. In addition, the paper shows a possibility of the resonant motion modes when using aerodynamic stabilization along the velocity vector. Relationships are obtained to determine critical values of the nanosatellite longitudinal angular velocity, where conditions for the resonant motion modes are met, and recommendations are provided for their prevention.

The study was supported by the Russian Science Foundation Grant no. 23-67-10007, https://rscf.ru/project/23-67-10007/

EDN XHCTPE

References
[1] Puig-Suari J., Turner C., Twiggs R. J. CubeSat: The development and launch support infrastructure for eighteen different satellite customers on one launch. In: 15th AIAA/USU Conference on Small Satellites, 2001.
[2] Puig-Suari J., Coelho R., Williams S. CubeSat design specification Rev. 14.1, CubeSat program. Cal. Poly SLO, 2022.
[3] Nanosats Database. Available at: https://www.nanosats.eu/ (accessed February 11, 2023).
[4] Selva D., Krejci D. A survey and assessment of the capabilities of CubeSats for Earth observation. Acta Astronautica, 2012, vol. 74, pp. 50–68.
[5] Simakov S.P., Ustyugov E.V. Opredelenie vzaimnogo polozheniya i orientatsii nanosputnikov po analizu videoizobrazheniy [Determination of relative position and orientation of nanosatellites by video image analysis]. Vestnik Samarskogo universiteta. Aerokosmicheskaya tekhnika, tekhnologii i mashinostroenie — Vestnik of Samara University. Aerospace and Mechanical Engineering, 2016, vol. 15, no. 1, pp. 122–131.
[6] Zharkikh R.N., Purikov A.V., Kuznetsov V.V., Shubin M.I., Svinareva A.M., Eletskaya L.L. Construction of wide-purpose space complexes based on the SXC6 platform. AIP Conference Proceedings, 2021, vol. 2318.
[7] Kim G.-N., Park S.-Y., Lee T., Kang D.-E., Jeon S., Son J., Kim N., Park Y.-K., Song Y. Development of CubeSat systems in formation flying for the solar science demonstration: The CANYVAL-C mission. Advances in Space Research, 2021, vol. 68, pp. 4434–4455.
[8] Fitzpatrick D.J., Palo S.E. Innovative systems engineering solutions for power-positive operations: navigating the multi-constraint challenges of the SWARM-EX CubeSat mission. Advances in Space Research, 2024. Available online 26 June 2024.
[9] Chernyshov A.A., Chugunin D.V., Mogilevsky M.M., Petrukovich A.A. Studies of the ionosphere using radiophysical methods on ultra-small spacecrafts. Acta Astronautica, 2020, vol. 167, pp. 455–459.
[10] Babanina O.V., Gasanbekov K.N., Prokhorenko I.S. Dvigatelnaya ustanovka korrektsii dlya nanosputnikov na freone [Correcting propulsion system for freon running nano-satellites]. Vestnik Moskovskogo aviatsionnogo instituta — Aerospace MAI Journal, 2023, vol. 30, no. 3, pp. 136–146.
[11] Sinitsyn L.I., Belokonov I.V. Vliyanie proizvodstvennykh otkloneniy elektro-termicheskoy dvigatelnoy ustanovki na tochnost manevrirovaniya nanosputnika [Influence of deviations in manufacturing of electrothermal propulsion system on nanosatellite maneuvering accuracy]. Vestnik Samarskogo universiteta. Aerokosmicheskaya tekhnika, tekhnologii i mashinostroenie — Vestnik of Samara University. Aerospace and Mechanical Engineering, 2021, vol. 20, no. 1, pp. 29–45.
[12] Poghosyan A., Golkar A. CubeSat evolution: analyzing CubeSat capabilities for conducting science missions. Progress in Aerospace Sciences, 2017, vol. 88, pp. 59–83.
[13] He L., Chen X., Kumar K. D., Sheng T., Yue C. et. al. A novel three-axis attitude stabilization method using in-plane internal mass-shifting. Aerospace Science and Technology, 2019, vol. 92, pp. 489–500.
[14] Chesi S., Gong Q., Romano M. Aerodynamic three-axis attitude stabilization of a spacecraft by center-of-mass shifting. Journal of Guidance, Control, and Dynamics, 2017, vol. 40, no. 7, pp. 1613–1626.
[15] Rawashdeh S.A. Attitude analysis of small satellites using model-based simulation. International Journal of Aerospace Engineering, 2019, vol. 2019, article ID 3020581, 11 p.
[16] Psiaki M.L. Nanosatellite attitude stabilization using passive aerodynamics and active magnetic torqueing. Journal of Guidance, Control, and Dynamics, 2004, vol. 27, no. 3, pр. 347–355.
[17] Belokonov I.V., Timbai I.A., Barinova E.V. Vybor proektnykh parametrov nanosputnika formata CubeSat s passivnoy sistemoy stabilizatsii [Design parameters selection for CubeSat nanosatellite with a passive stabilization system]. Giroskopiya i navigatsiya — Gyroscopy and Navigation, 2020, vol. 11, no. 2, pp. 149–161.
[18] Beletskiy V.V. Dvizhenie iskusstvennogo sputnika otnositelno tsentra mass [Artificial satellite motion relative to the center of mass]. Moscow, Nauka Publ., 1965, 416 p.
[19] Sarychev V.A., Ovchinnikov M.Yu. Dinamika sputnika s passivnoy aerodinamicheskoy sistemoy orientatsii [Dynamics of a satellite with the passive aerodynamic orientation system]. Kosmicheskie issledovaniya — Cosmic Research, 1994, vol. 32, no. 6, pp. 561–575.
[20] Sarychev V.A., Gutnik S.A. Dinamika sputnika pod deystviem gravitatsionnogo i aerodinamicheskikh momentov. Issledovanie ustoychivosti polozheniy ravnovesiya [Dynamics of satellite subject to gravitational and aerodynamic torques. Investigation of equilibria]. Kosmicheskie issledovaniya — Cosmic Research, 2016, vol. 54, no. 5, pp. 415–426.
[21] Barinova E.V., Timbai I.A. Polozhenie otnositelnogo ravnovesiya dinamicheski simmetrichnogo nanosputnika formata CubeSat pod deystviem gravitatsionnogo i aerodinamicheskogo momentov [Relative equilibria of dynamically symmetric CubeSat nanosatellite under the action of aerodynamic and gravitational torques]. Vestnik Samarskogo universiteta. Aerokosmicheskaya tekhnika, tekhnologii i mashinostroenie — Vestnik of Samara University. Aerospace and Mechanical Engineering, 2019, vol. 18, no. 2, pp. 21–32.
[22] Barinova E.V., Timbai I.A. Determining of equilibrium positions of CubeSat nanosatellite under the influence of aerodynamic and gravitational moments. In: 27th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2020. Proceedings, 2020. https://doi.org/10.23919/ICINS43215.2020.9133842
[23] Yaroshevsky V.A. Dvizhenie neupravlyaemogo tela v atmosphere [Motion of an uncontrolled body in the atmosphere]. Moscow, Mashinostroenie Publ., 1978.
[24] Aslanov V.S., Boiko V.V. Nonlinear resonant motion of an asymmetrical spacecraft in the atmosphere. Kosmicheskie issledovaniya — Cosmic Research, 1985, vol. 23, no. 3, pp. 408–415.
[25] Zabolotnov Yu.M., Lyubimov V.V. Primenenie metoda integraknykh mnogoobrazii dlya postroyeniya rezonansnykh krivykh v zadache vkhoda KA v atmosferu [Application of the integral manifold methods in construction of the resonant curves for the problem of spacecraft entry into the atmosphere]. Kosmicheskie issledovaniya — Cosmic Research, 2003, vol. 41, no. 5, pp. 481–487.
[26] Belokonov I.V., Timbai I.A., Nikolaev P.N. Analiz i sintez dvizheniya aerodinamicheski stabilizirovannykh kosmicheskikh apparatov nanoklassa formata CubeSat [Analysis and Synthesis of Motion of Aerodynamically Stabilized Nanosatellites of the CubeSat Design]. Giroskopiya i navigatsiya — Gyroscopy and Navigation, 2018, vol. 26, no. 3 (102), pp. 69–91.
[27] Barinova E.V., Belokonov I.V., Timbai I.A. Predotvrashchenie vozmozhnosti vozniknoveniya rezonansnykh rezhimov dvizheniya dlya nizkovysotnykh sputnikov klassa CubeSat [Preventing resonant motion modes for low-altitude CubeSat nanosatellites]. Giroskopiya i navigatsiya — Gyroscopy and Navigation, 2021, vol. 12, no. 4, pp. 1–19.
[28] Barinova E.V., Belokonov I.V., Timbai I.A. Motion features of aerodynamically stabilized Cubesat 6U nanosatellites. In: 29th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2022. Proceedings, 2022. https://doi.org/10.23919/ICINS51784.2022.9815390
[29] Aslanov V.S. Prostranstvennoe dvizhenie tela pri spuske v atmosfere [Spatial motion of a body during descent in the atmosphere]. Moscow, Fizmatlit Publ., 2004.
[30] Gantmakher F.R. Lektsii po analiticheskoy mekhanike [Lectures on analytical mechanics]. Moscow, Nauka Publ., 1966.
[31] Platus D.H. Dispersion of spinning missiles due to lift non-averaging. AIAA J., 1977, vol. 15, no. 7, pр. 909–915.