On the attitude motion of an orbiting rigid body under the influence of gravity gradient torque
Abstract
An investigation is made of the rotational motion of a rigid body orbiting the earth, under the influence of the geogravitygradient torque. The attitude dynamics are formulated as perturbations from a nominal case. The perturbed equations are solved asymptotically, by the multiple scales technique. The independent variable, time, is extended into a space of higher dimension by means of new scales, fast, slow, etc. Integration of the equations is carried out separately in the new variables. The rapid and slow aspects of the attitude dynamics are systematically separated, resulting in a more efficient computer implementation and enhanced physical insight. The theory is applied to predict the attitude dynamics of an asymmetric rigid body satellite. A comparison is made of the maximum errors as the step size increases as predicted by the multiple scales solution and direct numerical integration. An improvement in computational speed of an order of magnitude is demonstrated.
 Publication:

AIAA, Astrodynamics Conference
 Pub Date:
 August 1978
 Bibcode:
 1978aiaa.confQ....T
 Keywords:

 Earth Orbits;
 Gravitational Effects;
 Gravity Gradient Satellites;
 Guidance (Motion);
 Satellite Attitude Control;
 Torque;
 Analysis (Mathematics);
 Angular Velocity;
 Asymptotes;
 Computerized Simulation;
 Control Simulation;
 Differential Equations;
 Equations Of Motion;
 Moments Of Inertia;
 Orbital Mechanics;
 Rotating Bodies;
 Satellite Rotation;
 Astrodynamics