VESTNIK of Samara University. Aerospace and Mechanical EngineeringVESTNIK of Samara University. Aerospace and Mechanical Engineering2542-04532541-7533Samara National Research University673810.18287/2541-7533-2019-18-2-21-32UnknownRelative equilibria of dynamically symmetric CubeSat nanosatellite under the action of aerodynamic and gravitational torquesBarinovaE. V.<p><span lang="EN-US">Candidate of Science (Engineering)<br />Associate Professor of the Department of Higher Mathematics</span></p>L5545@yandex.ruTimbaiI. A.<p><span lang="EN-US">Doctor of Science (Engineering), Professor<br />Professor of Inter-University Department of Space Research</span></p>timbai@mail.ruSamara National Research University0307201918221320207201902072019Copyright © 2019, VESTNIK of Samara University. Aerospace and Mechanical Engineering2019<p>Motion of a dynamically symmetric CubeSat nanosatellite around the mass center on the circular orbit under the action of aerodynamic and gravitational torques is considered. We determined the nanosatellite equilibrium positions in the flight path axis system. We took into account the fact that the CubeSat nanosatellite has a rectangular parallelepiped shape and, therefore, the aerodynamic drag force coefficient depends on the angles of attack and proper rotation. We obtained formulae which allow calculating the values of the angles of attack, precession and proper rotation that correspond to the equilibrium positions, depending on the mass-inertia and geometric parameters of the nanosatellite, the orbit altitude, and the atmospheric density. It is shown that if the gravitational moment predominates over the aerodynamic one, there are 16 equilibrium positions, if the aerodynamic moment predominates over the gravitational one, there are 8 equilibrium positions, and in the case when both moments have comparable values there are 8, 12 or 16 equilibrium positions. Using the formulae obtained, we determined the equilibrium positions of the SamSat-QB50 nanosatellite. We calculated the ranges of altitudes where SamSat-QB50 nanosatellite has 8, 12, or 16 relative equilibrium positions.</p>Наноспутник формата CubeSatположения углового равновесияаэродинамический моментгравитационный моментугол атакиугол прецессииугол собственного вращенияCubeSat nanosatelliteangular equilibrium positionsaerodynamic momentgravitational torqueangle of attackangle of precessionangle of proper rotation[1. Sarychev V.A., Gutnik S.A. Dynamics of an axisymmetric satellite under the action of gravitational and aerodynamic torques. Cosmic Research. 2012. V. 50, Iss. 5. P. 367-375. DOI: <a href='http://doi.org/10.1134/S0010952512050061'>10.1134/S0010952512050061</a>][2. Sarychev V.A., Mirer S.A., Degtyarev A.A., Duarte E.K. Investigation of equilibria of a satellite subjected to gravitational and aerodynamic torques. Celestial Mechanics and Dynamical Astronomy. 2007. V. 97, Iss. 4. P. 267-287. DOI: <a href='http://doi.org/10.1007/s10569-006-9064-3'>10.1007/s10569-006-9064-3</a>][3. Sarychev V.A., Gutnik S.A. Dynamics of a satellite subject to gravitational and aero-dynamic torques. Investigation of equilibrium positions. Cosmic Research. 2015. V. 53, Iss. 6. P. 449-457. DOI: <a href='http://doi.org/10.1134/S0010952515060064'>10.1134/S0010952515060064</a>][4. Beletskiy V.V. Dvizhenie iskusstvennogo sputnika otnositel'no tsentra mass [Motion of an artificial satellite relative to the center of mass]. Moscow: Nauka Publ., 1965. 416 p.][5. Belokonov I.V., Kramlikh A.V., Timbai I.A. Low-orbital transformable nanosatellite: Research of the dynamics and possibilities of navigational and communication problems solv-ing for passive aerodynamic stabilization. Advances in the Astronautical Sciences. 2015. V. 153. P. 383-397.][6. Gantmakher F.R. Lektsii po analiticheskoy mekhanike [Lectures on analytical me-chanics]. Moscow: Nauka Publ., 1966. 300 p.][7. Shakhmatov E., Belokonov I., Timbai I., Ustiugov E., Nikitin A., Shafran S. SSAU project of the nanosatellite SamSat-QB50 for monitoring the Earth's thermosphere parameters. Procedia Engineering. 2015. V. 104. P. 139-146. DOI: <a href='http://doi.org/10.1016/j.proeng.2015.04.105'>10.1016/j.proeng.2015.04.105</a>][8. GOST 4401-81. Standard atmosphere. Parameters. Moscow: Izdatel'stvo Standartov Publ., 1981. 181 p. (In Russ.)]