圆型限制性三体问题的动力学特征

Dynamics characteristics of circular restricted three-body problem

禁行域在圆型限制性三体问题中对第三体的运动有极为重要的影响.利用零速度曲线讨论天体禁行域与系统参数之间的关系.禁行域与雅可比常数有关,且能影响天体的运动区域和轨道构型.利用最大李雅普诺夫指数寻找该模型的混沌轨道,给出混沌轨道在不同系统参数下随天体初始位置的分布.这些分布说明,当第三天体从两主天体连线的中点处释放时,容易产生混沌运动;当质量参量足够小时,体系无法产生混沌现象.

The forbidden zone has a significantly important influence on the motion of the third body in the circular restricted three-body problem.Based on zero-velocity curves,the relationship between the forbidden zone of celestial bodies and dynamical parameters was discussed.It was obtained that the forbidden zones are related to the Jacobian constant,and can affect motion areas of celestial bodies and dynamical types of orbits.The maximum Lyapunov exponents were used to find chaotic orbits,and the distributions of chaotic orbits with respect to the initial positions of the celestial bodies for different dynamical parameters were given.These distributions indicate that when the third celestial body is released from the midpoint of the two main celestial bodies,chaos easily occurs.However,there is no chaos when the mass parameter is small sufficiently.