长期非共面双行星问题的平衡
Equilibria in the secular, non-coplanar two-planet problem
摘要：
我们调查的长期动力学的行星系统组成的母恒星和两个大质量的行星在相互倾斜的轨道。在半长轴比（0.1-0.667）和行星质量比（0.25-2）的宽范围内，以及在整个允许的能量和总角动量范围内的动力学进行了研究。长期模型是由三体系统的半解析平均。我们专注于平衡的长期哈密顿（周期解的完整系统），我们分析其稳定性。我们试图分类家庭的这些解决方案的角动量积分。我们发现了新的平衡，但在文献中未知。我们的结果是一般性的，可以应用到广泛的一类三体系统，包括配置与恒星和棕矮星和亚恒星物体。我们还描述了一些技术方面的半数值平均。HD 12661行星系统作为一个例子进行了研究。
英文摘要：
We investigate the secular dynamics of a planetary system composed of the parent star and two massive planets in mutually inclined orbits. The dynamics are investigated in wide ranges of semi-major axes ratios (0.1-0.667), and planetary masses ratios (0.25-2) as well as in the whole permitted ranges of the energy and total angular momentum. The secular model is constructed by semi-analytic averaging of the three-body system. We focus on equilibria of the secular Hamiltonian (periodic solutions of the full system), and we analyze their stability. We attempt to classify families of these solutions in terms of the angular momentum integral. We identified new equilibria, yet unknown in the literature. Our results are general and may be applied to a wide class of three-body systems, including configurations with a star and brown dwarfs and sub-stellar objects. We also describe some technical aspects of the semi-numerical averaging. The HD 12661 planetary system is investigated as an example configuration.
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