Parametric and classical resonance in passive satellite aerostabilization

Purely passive aerostabilization of satellites has never been flight demonstrated. The Shuttle hitchhiker passive aerodynamically stabilized magnetically damped satellite experiment would be the first flight experiment of its kind that, in conjunction with results from a high-fidelity computer simulator, would corroborate attitude stability. Pure aerostabilization, with no gravity gradient restoring torques, if proved, is highly desirable for future missions such as the gravity and magnetic Earth surveyor. High-fidelity nonlinear simulation results indicate interesting attitude behavior, such as cone angle transients that provoke the need for sound theoretical justification. A wind vane in a wind field model is used to derive simple analogous Mathieu-Hill equations of motion, the stability properties of which are predicted via Floquet theory. Parametric resonance caused by higher order of the once per orbit density harmonics, varying natural frequency of oscillation as a result of altitude decay, and varying wind magnitude due to global winds are studied in detail. The simple time-varying linear wind vane analogy captures the essence of the observations made with the complex nonlinear simulation. Classical resonance because of step changes in the solar torques as a result of Earth occultation is also discussed. Based on insight obtained from the stability properties observed for the wind vane analogy, an optimal satellite is designed that provides best attitude performance while maintaining sufficient lifetime and other mission constraints. Nomenclature : area of analogous wind vane, m2 = average ballistic coefficient of subsat, kg/m2 = moment of inertia about an axis of rotation, kg-m2 : aerodynamic moment stiffness, N-m/rad = length of back shell, cm : length of front shell, cm : mass of subsat, kg = center-of-pres sure to center-of-mas s offset, m = inner radius of front shell, cm : aerodynamic torque, N-m : thickness of back shell, cm : thickness of front shell, cm = velocity magnitude of wind, m/s = cone angle of the satellite, rad : damping ratio = coefficient of damping, N-m-s/rad = angle of rotation of wind vane from reference wind direction, rad = density of air, kg/m3 = amplitude of once/orbit harmonic of Q, kg/m3 = density of back shell, kg/m3 = bias component of density of air profile over one orbit, kg/m3 = density of front shell, kg/m3 = accommodation coefficients = natural frequency of oscillation of wind vane, rad/s = once per orbit frequency, rad/s