| Abstract: | The attitude stability of an Earth-orbiting satellite experiencing aerodynamic torque is studied. This is accomplished by applying the theory of total stability (or, stability under constantly acting disturbances) to the equations of motion. The satellite is gravity-gradient stabilized and a damping torque is incorporated. The aerodynamic torque results from the presence of two flat panels attached to the cylindrical body of the vehicle. This perturbing torque is treated as an additive disturbance in Euler's equations of motion. A Lyapunov function is constructed and then used in an appropriate theorem on stability under constantly acting disturbances. Explicit expressions are thereby found for bounds on a hypothetical initial condition (a rotation from the Earth-pointing equilibrium) and on the aerodynamic torque, so that if these disturbances are less than their respective bounds then the resulting attitude motion of the satellite will not exceed a pre-assigned value. These bounds depend on that pre-assigned value, and on the physical parameters of the satellite. The design implications of these bounds are then discussed. |
