MEO区域的动力学结构：长期稳定性、混沌和输运
The dynamical structure of the MEO region: long-term stability, chaos, and transport
摘要：
长期以来，人们一直怀疑全球导航卫星系统存在于复杂共振和混沌运动的背景中;然而，这些现象的精确动力学特征仍然难以捉摸。最近的研究表明，驱动这些动力学的共振的发生和性质主要取决于节点和拱点岁差的频率以及月球节点的回归率。编织在整个倾角和偏心率相空间是一个非常复杂的网状结构的日月长期共振，这变得特别密集的导航卫星轨道的倾角附近。清楚地了解这些共振的物理意义对于设计四个星座的处置策略具有相当大的实际意义。在这里，我们提出的分析和半分析模型，准确地反映了共振相互作用的真实性质，并跟踪拓扑组织的流形上发生的混沌运动。我们提出了一个图集的FLI稳定性地图，显示的程度的相空间的混沌区域，计算通过层次结构的更现实，更复杂的模型，并比较这些图表中的混沌区域的宽度的分析估计的启发式Chirikov共振重叠准则的混沌层。由于卫星的半长轴后退，我们观察到从稳定的Nekhoroshev样结构在三个地球半径，其中规则的轨道占主导地位，到一个Chirikov政权的共振重叠在五个地球半径的过渡。从数值估计的李雅普诺夫时间，我们发现，许多倾斜的，近圆形轨道的导航卫星是强烈的混乱，他们的动态是不可预测的十年的时间尺度。
英文摘要：
It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Recent studies have shown that the occurrence and nature of the resonances driving these dynamics depend chiefly on the frequencies of nodal and apsidal precession and the rate of regression of the Moon's nodes. Woven throughout the inclination and eccentricity phase space is an exceedingly complicated web-like structure of lunisolar secular resonances, which become particularly dense near the inclinations of the navigation satellite orbits. A clear picture of the physical significance of these resonances is of considerable practical interest for the design of disposal strategies for the four constellations. Here we present analytical and semi-analytical models that accurately reflect the true nature of the resonant interactions, and trace the topological organization of the manifolds on which the chaotic motions take place. We present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance-overlap criterion. As the semi-major axis of the satellite is receding, we observe a transition from stable Nekhoroshev-like structures at three Earth radii, where regular orbits dominate, to a Chirikov regime where resonances overlap at five Earth radii. From a numerical estimation of the Lyapunov times, we find that many of the inclined, nearly circular orbits of the navigation satellites are strongly chaotic and that their dynamics are unpredictable on decadal timescales.
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