椭圆型三体约束问题三角点的稳定性图
Stability chart of the triangular points in the elliptic restricted problem of three bodies
摘要：
对类特洛伊太阳系外行星的可能观测，促进了对共轨共振运动稳定性行为的更深入理解。利用Hill方程和能量率法对椭圆型限制性三体问题的稳定性映射进行了分析。区域的$μ-e$参数平面的数值描述和相关的共振频率的librational运动。因此，稳定性和不稳定性可以通过分析取决于系统参数的两个独立的频率模式来获得。证明了长周期天平动在确定稳定性结构中的关键作用，并发现了一种稳定性机制，该机制负责延长测试粒子在稳定性图的不稳定域中的寿命。
英文摘要：
The possible observations of Trojan-like extrasolar planets stimulate the deeper understanding of the stability behaviour of the co-orbital resonant motion. By using Hill's equations and the energy-rate method an analysis of the stability map of the elliptic restricted three-body problem is performed. Regions of the $μ-e$ parameter plane are described numerically and related to the resonant frequencies of librational motion. Stability and instability can therefore be obtained by analysing the two independent frequency modes depending on system parameters. The key role of the long period libration in determining the structure of the stability is demonstrated and also a stability mechanism is found that is responsible for extended life time of the test particle in the unstable domain of the stability map.
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