论文标题
磁盘引起的重力扰动的轨道动力学
Orbital Dynamics with the Gravitational Perturbation due to a Disk
论文作者
论文摘要
本文通过分析和数值方法研究了由于二维均匀磁盘引起的重力扰动下轨道的世俗行为。我们开发了此问题的世俗近似，并首先获得该系统的平均哈密顿量。 We find that, when the ratio of the semimajor axes of the inner orbit and the disk radius takes very small values ($\ll1$), and if the inclination between the inner orbit and the disk is greater than the critical value of $30^\circ$, the inner orbit will undergo the (classical) Lidov-Kozai resonance in which variations of eccentricity and inclination are usually very large and the system has two $ω=π/2,3π/2 $（$ω$的平衡点是圆周的参数）。随着比率增加到0.4，临界值将略有下降至$ 27^\ Circ $。但是，外轨道不会产生世俗的共振，偏心和倾斜度的变化很小。当轨道和磁盘半径的比率接近$ 1 $时，还有许多复杂的利多夫 - 科泽共振类型，导致轨道行为与经典的利多夫 - 科扎伊案例不同。在这些共振中，系统具有更多的平衡点，可能出现在$ω= 0，π/2，π，3π/2 $，甚至其他值为$ω$。此外，偏心率和倾斜度的变化变得相对温和，在某些情况下，轨道可以保持在高度倾斜的状态。此外，分析表明，Kuzmin磁盘也可以导致（经典的）Lidov-Kozai共鸣，而关键倾向也是$ 30^\ Circ $。
The secular behavior of an orbit under the gravitational perturbation due to a two-dimensional uniform disk is studied in this paper, through analytical and numerical approaches. We develop the secular approximation of this problem and obtain the averaged Hamiltonian for this system first. We find that, when the ratio of the semimajor axes of the inner orbit and the disk radius takes very small values ($\ll1$), and if the inclination between the inner orbit and the disk is greater than the critical value of $30^\circ$, the inner orbit will undergo the (classical) Lidov-Kozai resonance in which variations of eccentricity and inclination are usually very large and the system has two equilibrium points at $ω=π/2,3π/2$ ($ω$ is the argument of perihelion). The critical value will slightly drop to about $27^\circ$ as the ratio increases to 0.4. However, the secular resonances will not occur for the outer orbit and the variations of the eccentricity and inclination are small. When the ratio of the orbit and the disk radius is nearly $1$, there are many more complicated Lidov-Kozai resonance types which lead to the orbital behaviors that are different from the classical Lidov-Kozai case. In these resonances, the system has more equilibrium points which could appear at $ω=0,π/2,π,3π/2$, and even other values of $ω$. The variations of eccentricity and inclination become relatively moderate, moreover, in some cases the orbit can be maintained at a highly inclined state. In addition, a analysis shows that a Kuzmin disk can also lead to the (classical) Lidov-Kozai resonance and the critical inclination is also $30^\circ$.
