椭圆Hill问题的动力学：周期轨道和稳定区域
The dynamics of the elliptic Hill problem : Periodic orbits and stability regions
摘要：
卫星绕行星的运动可以通过希尔模型来研究，希尔模型是关于卫星绕行星运动的限制性三体问题的修改。虽然文献中对圆形Hill模型的动力学进行了广泛的研究，但到目前为止，关于椭圆模型的动力学只有很少的结果，即运动方程和少数不稳定的周期轨道族。在本研究中，我们通过计算大量的周期轨道族及其线性稳定性来扩展这些结果，并根据它们的共振条件对它们进行分类。虽然它们中的大多数是不稳定的，但我们能够找到相当数量的稳定的。通过计算适当的动力学稳定性图，研究了行星偏心率对卫星轨道稳定性的影响。我们看到，即使对于大的行星偏心率值，规则轨道可以在稳定的周期轨道附近找到。大多数不规则轨道是逃逸轨道。
英文摘要：
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model have been extensively studied in the literature, only few results about the dynamics of the elliptic model were known up to now, namely the equations of motion and few unstable families of periodic orbits. In the present study we extend these results by computing a large set of families of periodic orbits and their linear stability and classify them according to their resonance condition. Although most of them are unstable, we were able to find a considerable number of stable ones. By computing appropriate maps of dynamical stability, we study the effect of the planetary eccentricity on the stability of satellite orbits. We see that, even for large values of the planetary eccentricity, regular orbits can be found in the vicinity of stable periodic orbits. The majority of irregular orbits are escape orbits.
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