Abstract: The singularity problem of orbital elements for describing the orbital motion of the spacecraft can be solved by quaternion method. Due to the inherent double value of the quaternion, it is difficult to select positive or negative value of the quaternion for the integration of the motion equation. The quaternionmethodology with a modified constraint equation was introduced to describe Lagrange′s planetary equations. The influence of the earth oblateness perturbation on the orbit of the geostationary satellite was researched. The results show that when the eccentricity is less than 1, the quaternion can be  used to solve singularity problem caused by orbital elements. Compared with the modified equinoctial orbit elements, the quaternion has a clearer  physical and geometrical interpretation. The variable motion equation with the quaternion can be calculated more simply and integrated more efficiently. In addition,the calculation error can also meet the requirements.

Key words: Orbital elements, Singularity, Quaternion method, Constraint, Lagrange′s planetary equations, Spacecraft