Semi-analytical attitude propagation for earth orbiting objects

This paper presents the development of a semi-analytical theory for the long-term propagation of the attitude motion of Earth-orbiting objects with arbitrary shape. The attitude dynamics includes the effects of gravity-gradient, residual magnetic, and light-pressure torques. The equations of motion are expressed in Sadov variables. The equations of motion are averaged over the Sadov angles and the orbital mean anomaly and a combination of Lie transformations is applied to transform from non-averaged to mean attitude variables. It will be shown how this technique can be used to estimate the approximation error and improve the accuracy of the averaged solution. Furthermore, we introduce an alternative set of variables, that removes one of the singularities in the formulation in Sadov variables. The results of the numerical tests demonstrate that the proposed semi-analytical theory, provides a good balance between accuracy and computational cost.