Periodic attitude motions of an axisymmetric spacecraft in an elliptical orbit near the hyperbolic precession

This paper deals with the existence and stability of periodic attitude motion near hyperbolic precession (HP) for a dynamically symmetric rigid body (RB) with its center of mass moving along an elliptical orbit. We present the definitions of undisturbed and disturbed periodic attitude motions, and approximate analytical solutions for them are derived using the multiscale method under non-resonance, internal resonance, and combination resonance conditions. Based on the definition of Lyapunov stability, we demonstrate stability in the non-resonant case and establish the conditions require for stability in the internal resonance scenario and a numerical analysis supports the theoretical results. The findings of this study extend classical results on RB dynamics in central gravitational fields. These insights demonstrate that appropriate parameter selection can achieve stable periodic attitude motion for RBs is in elliptical orbits, offering practical implications for spacecraft attitude control and mission reliability.