Semi-analytical investigations on the dynamics of BeiDou inclined geosynchronous satellite orbit

Abstract

A semi-analytical investigation on the dynamics of BeiDou IGSO is conducted in this paper. First, a semi-analytical propagator is constructed based on the mean element method. The comparison of results of semi-analytical propagation with reference orbits shows that all orbital elements except the semi-major axis agree well within six centuries. For some example orbits, the semi-analytical propagation of the semi-major axis is accurate only within several decades, which is related to the chaotic motion of the one-to-one tesseral resonance. Compared with the numerical ephemeris of Moon, an improvement of accuracy in the semi-analytical propagation is observed when a simple analytical ephemeris of Moon is adopted. This phenomenon agrees with the doubly averaging process of the third-body perturbation. Second, the dynamics of BeiDou IGSO are investigated using the Hamiltonian approach with simplified models. The transition between different resonance regions of one-to-one tesseral resonance is investigated by the computation of one-dimensional maximal Lyapunov characteristic exponent (1-mLCE). The secular resonance from the lunisolar perturbation modeled by a 2-DOF system is systematically investigated using the surface of section. The secondary resonance related to the precession of lunar node is identified by the computation of 1-mLCE. In the end, the reentry disposal for BeiDou IGSO is investigated as an optimization problem. With IGSO3 as an example of reentry orbit, the sensitivity analysis is conducted to study its stability and predictability.