自旋-自旋模型与双同步共振俘获
The spin-spin model and the capture into the double synchronous resonance
摘要：
本文的目的是提出一个模型，这是一个平面版本的完整的两体问题，并讨论相关的周期解的存在性和稳定性。考虑两个在固定共面开普勒轨道上相互绕转的均匀椭球。此外，假设它们各自的自旋轴垂直于轨道平面，轨道平面也是共同的赤道平面。自旋-自旋模型处理两个椭球体的耦合旋转动力学。对于非零轨道偏心率，它具有非自治耦合摆系统的结构。这个模型是经典的两个扩展体的自旋轨道问题的自然扩张。此外，我们考虑耗散潮汐扭矩，可以触发捕获系统的自旋轨道和自旋自旋共振。本文给出了守恒模型和耗散模型的一些理论结果。保守模型具有哈密顿结构。利用哈密顿系统的性质，在参数空间中给出了该模型奇周期解的存在性、唯一性和线性稳定性的充分条件.这个解决方案代表了一个双同步共振的保守制度。这样的解可以继续到耗散区，在那里它变得渐近稳定。我们将渐近稳定性看作是捕获到双同步共振的动力学机制。最后，我们将我们的结果应用到几个案例，包括冥王星-冥卫一二进制和特洛伊双星小行星617帕特洛克罗斯，LUCY任务的目标。
英文摘要：
The aim of this article is to propose a model, that is a planar version of the Full Two-Body Problem, and discuss the existence and stability of a relevant periodic solution. Consider two homogeneous ellipsoids orbiting around each other in fixed coplanar Keplerian orbits. Moreover, their respective spin axes are assumed to be perpendicular to the orbital plane, that is also a common equatorial plane. The spin-spin model deals with the coupled rotational dynamics of both ellipsoids. For a non-zero orbital eccentricity, it has the structure of a non-autonomous system of coupled pendula. This model is a natural extension of the classical spin-orbit problem for two extended bodies. In addition, we consider dissipative tidal torques, that can trigger the capture of the system into spin-orbit and spin-spin resonances. In this paper we give some theoretical results for both the conservative model and the dissipative one. The conservative model has a Hamiltonian structure. We use properties of Hamiltonian systems to give some sufficient conditions in the space of parameters of the model, that guarantee existence, uniqueness and linear stability of an odd periodic solution. This solution represents a double synchronous resonance in the conservative regime. Such solution can be continued to the dissipative regime, where it becomes asymptotically stable. We see asymptotic stability as a dynamical mechanism for the capture into the double synchronous resonance. Finally we apply our results to several cases including the Pluto-Charon binary system and the Trojan binary asteroid 617 Patroclus, target of the LUCY mission.
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