挠性联结双体航天器的稳定性与分岔

STABILITY AND BIFURCATION OF TWO-BODY SATELLITE WITH FLEXIBLE CONNECTION

研究圆轨道内受万有引力矩作用的挠性联结双体航天器在轨道平面内的姿态运动，讨论其相对轨道坐标系平衡状态的稳定性与分岔．提出判别平衡方程非平凡解存在性的几何方法，并应用Ｌｉａｐｕｎｏｖ直接法、Ｌｉａｐｕｎｏｖ－Ｓｃｈｍｉｄｔ约化方法和奇异性理论导出解析形式的稳定性与分岔的充要条件。

The planar attitude motion of a two-body satellite with flexible connection subject to the gravitational torque in a circular orbit is studied in this paper. The relative equilibrium equations in the orbital coordinate frame are derived and the trivial solutions of the equations are corresponding to the normal working states. A geometric method to determine the conditions of existence of nontrivial solutions is proposed. By using Liapunov-Schmidt reduction method and singularity theory, the conditions of occurrence of bifurcation from trivial solutions in analytical form are derived, and the type of bifurcation is proved to be pitchfork-bifurcation. Finally Liapunov's direct method is used in the analysis of the stability of each relative equilibrium state and a stability diagram in parameters plane is presented, thus the global behavior of the motion of the system is described qualitatively. The study shows that: (a) The attitude motion of a two-body system in the gravitational field takes on complex dynamic behavior. The stable domains of the trivial solutions in the parameters plane are determined by mass geometry of each body and the stiffness coefficient of the flexible connection. (b) The geometric method proposed in this paper can be used to judge the existence of nontrivial solutions effectively. In this case positions of occurrence of bifurcation correspond to the border curves of existence domains of nontrivial solutions.