万有引力场中挠性联结双体系统的稳定性与分岔

STABILITY AND BIFURCATION OF TWO-BODY SYSTEM WITH FLEXIBLE CONNECTION IN GRAVITATIONAL FIELD

本文讨论受万有引力矩作用沿圆轨道运动的挠性联结双体系统的平面天平动。讨论其相对轨道坐标系的可能平衡状态,利用Liapuaov直接法分析各平衡状态的稳定性。分析表明,当刚度系数足够小时,平衡状态可产生分岔和稳定性突变。利用参数空间对系统的全局运动性态作出定性的描述。

In this paper, the planar libration of a two-body system with flexible connection in circular orbit under the application of the gravitational torque is discussed. All possible equilibrium states relative to the orbital coordinates have been considered. The stability of each state is analyzed by the use of the Liapunov's direct method. It is shown that a bifurcation of equilibrium state and its stability may take place when the stiffness coefficient is small enough. Taking advantage of the parameter's space the global motion of the system can be described qualitatively.