Analytical Identification of Periodic Orbit–Attitude Motions in the Sun–Earth System

Achieving a coupled periodic solution is crucial for reducing the need for additional control to maintain attitude stability. However, the formulation of such a solution heavily depends on an accurate initial guess due to the complex dynamics. This paper proposes a predict–search–correct approach for identifying coupled periodic solutions along periodic orbits in the Sun–Earth system. The main contributions of this study are summarized as follows: First, analytical conditions for coupled periodic motion are formulated, enabling the prediction of feasible initial states with arbitrarily prescribed attitudes. Second, a prediction-based search method is developed by integrating the analytical conditions with the Poincaré mapping framework, which significantly reduces the search range and computational cost. Third, a new type of coupled periodic motion, referred to as attitude equilibrium motion, is discovered, analytically characterized, and successfully identified along planar Lyapunov orbits, thereby expanding the solution space for periodic orbit–attitude motion. This expanded solution space enables a wider range of orbit–attitude configurations for future space telescopes operating near the libration points of the Sun–Earth three-body system.