Miranda动力学历史的数值研究
A numerical exploration of Miranda's dynamical history
摘要：
天王星的卫星米兰达呈现出高倾角（4.338°）和表面重塑的证据。20年来，人们一直认为这种倾向是由于过去陷入了与Umbriel的3：1共振中（例如Tittemore和Wisdom 1989，Malhotra和Dermott 1990）。最近几年，人们对天王星系统重新产生了兴趣，因为哈勃太空望远镜允许探测到一个由环和小的嵌入式卫星组成的内部系统，它们的动力学当然受到主要卫星的控制。出于这个原因，我们在这里建议重新审视米兰达的长期动态，使用现代工具，如密集的计算设施和新的混沌指标（MEGNO和频率图分析）。与之前的研究一样，我们发现了导致米兰达倾角的共振和相关的次级共振，可能已经阻止了米兰达倾角在4.5°的上升。此外，我们还得到了这种倾角达到7°的其他轨迹。基于Moons和Henrard（1993）的研究，我们还提出了对相关次级共振的分析研究。
英文摘要：
The Uranian satellite Miranda presents a high inclination (4.338°) and evidences of resurfacing. It is accepted since 20 years (e.g. Tittemore and Wisdom 1989, Malhotra and Dermott 1990) that this inclination is due to the past trapping into the 3:1 resonance with Umbriel. These last years there is a renewal of interest for the Uranian system since the Hubble Space Telescope permitted the detection of an inner system of rings and small embedded satellites, their dynamics being of course ruled by the main satellites. For this reason, we here propose to revisit the long-term dynamics of Miranda, using modern tools like intensive computing facilities and new chaos indicators (MEGNO and frequency map analysis). As in the previous studies, we find the resonance responsible for the inclination of Miranda and the secondary resonances associated, likely to have stopped the rise of Miranda's inclination at 4.5°. Moreover, we get other trajectories in which this inclination reaches 7°. We also propose an analytical study of the secondary resonances associated, based on the study by Moons and Henrard (1993).
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