HOVERING ORBITS DESIGN FOR PERTURBED ASTEROIDS WITH PARAMETRIC EXCITATION RESONANCE

In this paper, the solar gravitational perturbation is considered as a part of the asteroid system instead of treating it as perturbation. Based on the concept of parametric excitation resonance in nonlinear vibration theory, a novel stable parametric resonance orbit near the equilibrium point is designed. In order to consider the gravitational field of an irregular asteroid and the gravitational force of the Sun, the perturbed particle-linkage model is adopted. By analyzing the equilibrium points and the natural frequencies of the unperturbed system, the preconditions that the parametric resonance periodic orbit can exist are given. Taking the second principal resonance and 1:3 internal resonance as examples, the steady-state solutions of parametric resonance orbit are obtained by using multi-scale method. The stability of the steady-state solution is determined. The nonlinear dynamic behaviors of the system are analyzed by the amplitude-frequency response curve. In addition, parametric excitation effect caused by solar gravitational perturbation and the energy transfer phenomenon between long and short periodic motions are analyzed. The proposed method of this paper can expand the existing periodic orbit families near asteroids.