Abstract
In this paper, the study of stabilization accuracy of a satellite equipped with a set of reaction wheels (RW) is presented. The model of motion takes into account possible static and dynamic reaction wheel imbalances. Due to the complexity of the model, which leads to the numerical issues, the effects of dynamic and static imbalances on inertial stabilization are studied analytically. As a result, estimations of the attitude and stabilization accuracy are presented in closed form.
Highlights
This paper studies the problem of the attitude and stabilization accuracy in fully coupled motion
Note that attitude stabilization accuracy depends on the RW position with respect to the system center of mass ρk, i.e., the farther RWs are placed from the system center of mass, the worse stabilization accuracy is
The difference can be explained by the gravity gradient torque which is included in the numerical model but is not taken into account in the analytical study. Both dynamic and static imbalances lead to the additional terms in the right parts of Equations (15) and (20), which do not depend on satellite state vector components for the first order approximation, so the total stabilization accuracy is the sum of Equations (17) and (21)
Summary
A precise mathematical model is rather complex, and it takes a considerable amount of time to implement it and conduct all the necessary Monte Carlo simulations to estimate the effect of imbalances This problem occurs because the more angular rate of the RW is—the more effect on the attitude would be. In the study of [26], the general approach to estimate the effect of disturbances on the attitude accuracy is suggested, but it works with a simple model of motion that does not take into account RW imbalances. The main goal of this paper is to obtain the end form expressions for the attitude and stabilization accuracy, which are useful for preliminary mission design They require neither program model implementation nor extensive numerical study
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