Relative equilibria of dynamically symmetric CubeSat nanosatellite under the action of aerodynamic and gravitational torques

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.