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The spin–spin model and the capture into the double synchronous resonance
Nonlinearity ( IF 1.7 ) Pub Date : 2021-04-22 , DOI: 10.1088/1361-6544/abc4d8
Mauricio Misquero

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.



中文翻译:

自旋-自旋模型和捕获到双同步共振

本文的目的是提出一个模型,即完整二体问题的平面版本,并讨论相关周期解的存在性和稳定性。考虑在固定的共面开普勒轨道中彼此绕行的两个同质椭球。此外,假设它们各自的自旋轴垂直于轨道平面,轨道平面也是一个共同的赤道平面。自旋-自旋模型处理两个椭球的耦合旋转动力学。对于非零轨道偏心率,它具有耦合摆的非自治系统的结构。该模型是两个扩展天体的经典自旋轨道问题的自然扩展。此外,我们考虑了耗散潮汐力矩,它可以触发系统捕获到自旋轨道和自旋自旋共振中。在本文中,我们给出了保守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。我们利用哈密顿系统的性质给出了模型参数空间中的一些充分条件,以保证奇周期解的存在性、唯一性和线性稳定性。这个解决方案代表了保守状态下的双同步共振。这种解可以继续到耗散状态,在那里它变得渐近稳定。我们将渐近稳定性视为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于几个案例,包括冥王星-卡戎双星系统和特洛伊双星小行星 617 Patroclus,LUCY 任务的目标。

更新日期:2021-04-22
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