Uniaxial aerodynamic attitude control of artificial satellites

Within the context of a simple mechanical model the paper examines the movement of a satellite with respect to the center of masses under conditions of uniaxial aerodynamic attitude control. The equations of motion of the satellite take account of the gravitational and restorative aerodynamic moments. It is presumed that the aerodynamic moment is much larger than the gravitational, and the motion equations contain a large parameter. A two-parameter integrated surface of these equations is constructed in the form of formal series in terms of negative powers of the large parameter, describing the oscillations and rotations of the satellite about its lengthwise axis, approximately oriented along the orbital tangent. It is proposed to treat such movements as nominal undisturbed motions of the satellite under conditions of aerodynamic attitude control. A numerical investigation is made for the above integrated surface.