On attitude dynamics of spin-stabilized satellite

Yu.V.Kim

Canadian Space Agency

St-Hubert, Québec, Canada J3Y 8Y9

 

Stabilization of satellite attitude by spinning in orbit is a simple but popular method used in many satellite designs. The method can be used in operational pointing mode when a single-axis of stabilization is only required, or in a back up safety mode (Safe Hold Mode-SHM), when only sufficient solar illumination conditions are needed for satellite solar panels to stay in this state for a long enough time without discharging batteries below a critical level. By this fashion the method is used in SHM of Earth observation Canadian satellite RADARSAT-1 that is currently operated by CSA.

For the new generation of small and micro-satellites that are being developed with CSA support, spin-stabilization method can provide a low cost but sound design. As a minimum, it can provide practically infinite duration of SHM with power positive conditions.

Spinning satellite attitude dynamics is a classical problem that has been discussed in details in books and in many articles.

In particular, the conditions of stability and capturing a spinning satellite by the gravity gradient torque had been obtained and have become classical. These conditions are applicable to considering satellite attitude in non-precessing (immovable in inertial spatial) orbit or, in another words, w.r.t some not rotating in inertial spatial direction.

In practice, however, the primary design driver is the capability of the satellite to follow in inertial space some rotating directions such as: sun direction or the normal to satellite orbit, which has slow precession caused by Earth oblateness effect. This issue of spinning satellite dynamics has been poorly considered in publications.

(only few articles can be referenced). It is apparent that spinning satellite can be considered as a free gyroscope with its angular momentum fixed in inertial space and drifting from any moving direction. In particular, drifting from the precessing orbit normal (being initially aligned with this direction). Being guided by this idea, some authors suggested adjusting satellite inertia, spinning rate and orbit inclination angle so that gravity gradient torque would compensate gyroscopic torque induced by the satellite rotation.

In this article, the behavior of spinning satellite with respect to precessing orbit is explained by the frequency properties of the dynamical system. It has been showed that this behavior can be explained from the position of oscillation theory considering beating effect of oscillations caused by the harmonical disturbance torques appearing in the equations of motion, when orbital precession effect is taken into account.

The oscillations will be close to the resonance effect if the ratio of satellite spinning rate to its orbital rate exceeds some certain margin. In this case satellite angular beat oscillations can be considered as a restricted drift of satellite angular momentum from its orbit normal. However, if the ratio doesn't exceed this margin, then amplitude modulated oscillations with a small amplitude will take place. In this case satellite angular momentum will practically precess synchronously with sun-synchronous orbit. The article includes the simulation work performed by the author devoted to the aforementioned issue of spinning satellite dynamics and experimental telemetry data, obtained from RADARSAT-1 SHM.