论文标题
非限制性分层行星系统中的四极杆和八杆序共振
Quadrupole and octupole order resonances in non-restricted hierarchical planetary systems
论文作者
论文摘要
非限制的分层三体构型在天体物理系统的各种尺度上很常见。在非限制的层次行星系统下，在这项工作中研究了四极级共振（von Zeipel-Lidov-kozai共振）和八杆级共振（APSIDAL共振）的动力结构。在四极阶汉密尔顿模型下，在保守量跨越的参数空间中，分析了库和循环区域的分布以及翻转区域的分布。产生了系统的基本频率，然后确定了Octupole-reser共振的标称位置。从扰动理论的角度来看，四极阶汉密尔顿人决定了不受干扰的动力学模型，而八极阶汉密尔顿人则起着对四极级动力学的扰动作用。八杆阶共振的共振汉密尔顿人是通过平均理论来提出的，从而产生了新的运动常数。产生相位肖像来分析八杆级共振的动态结构，包括共振中心，鞍点，动力学分离和库的岛屿。通过分析相肖像，发现图书馆中心有四个分支和八个图书馆区域。轨道翻转的应用表明，有五个翻转区域。
Nonrestricted hierarchical three-body configurations are common in various scales of astrophysical systems. Dynamical structures of the quadrupole-order resonance (the von Zeipel-Lidov-Kozai resonance) and the octupole-order resonance (the apsidal resonance) under the nonrestricted hierarchical planetary systems are investigated in this work by taking advantage of perturbative treatments. Under the quadrupole-order Hamiltonian model, the distribution of libration and circulation regions as well as the distribution of flipping region are analytically explored in the parameter space spanned by the conserved quantities. The fundamental frequencies of system are produced and then the nominal location of octupole-order resonance is identified. From the viewpoint of perturbative theory, the quadrupole-order Hamiltonian determines the unperturbed dynamical model and the octupole-order Hamiltonian plays an role of perturbation to the quadrupole-order dynamics. The resonant Hamiltonian for octupole-order resonances is formulated by means of averaging theory, giving rise to a new constant of motion. Phase portraits are produced to analyse dynamical structures of octupole-order resonance, including resonant centres, saddle points, dynamical separatrices and islands of libration. By analysing phase portraits, it is found that there are four branches of libration centre and eight libration zones in the considered space. Applications to orbit flips show that there are five flipping regions.
