非轴对称引力势中的共振
Resonances in non-axisymmetric gravitational potentials
摘要：
我们研究的扇形共振的形式$jκ= m(n-Ω)$周围的非轴对称体的自旋率$Ω$，其中$κ$和$n$是周转频率和平均运动的粒子，分别，其中$j>0$和$m$（$<0$或$>0$）是整数，$j$是共振阶。这描述了正转半径内和正转半径外的$n/Ω\sim m/(m-j)$共振，以及逆转和逆转共振。结果表明：（1）周期轨道的运动学只依赖于$(m,j)$的不可约（互质）形式$(m',j')$.在旋转坐标系中，周期轨道有$j'$辫、$|m'|$相同扇区和$|m'|(j'-1)$自交叉点;（2）因此，Lindblad共振（与$j=1$）没有自交叉点;（3）具有相同$j'$和相反$m'$的共振具有相同的运动学，并被称为$twins$ ;（4）给定$n/Ω$的共振阶数取决于势的对称性。在$2π/k$ -旋转下不变的势仅产生与$m$的$k$倍数的共振;（5）具有相同$j$和相反$m$的共振具有相同的运动学和相同的动力学，并且被称为$true~twins$ ;（6）逆行共振（$n/Ω< 0$）总是比它的前一个对应物高阶（$n/Ω> 0$）;（7）利用经典的摄动算子，可以用一种紧凑的形式计算卫星的共振强度。对Chariklo和Haumea进行了应用。
英文摘要：
We study sectoral resonances of the form $jκ= m(n-Ω)$ around a non-axisymmetric body with spin rate $Ω$, where $κ$ and $n$ are the epicyclic frequency and mean motion of a particle, respectively, where $j>0$ and $m$ ($<0$ or $>0$) are integers, $j$ being the resonance order. This describes $n/Ω\sim m/(m-j)$ resonances inside and outside the corotation radius,as well as prograde and retrograde resonances. Results are: (1) the kinematics of a periodic orbit depends only on $(m',j')$, the irreducible (relatively prime) version of $(m,j)$. In a rotating frame, the periodic orbit has $j'$ braids, $|m'|$ identical sectors and $|m'|(j'-1)$ self-crossing points; (2) thus, Lindblad resonances (with $j=1$) are free of self-crossing points; (3) resonances with same $j'$ and opposite $m'$ have the same kinematics, and are called $twins$; (4) the order of a resonance at a given $n/Ω$ depends on the symmetry of the potential. A potential that is invariant under a $2π/k$-rotation creates only resonances with $m$ multiple of $k$; (5) resonances with same $j$ and opposite $m$ have the same kinematics and same dynamics, and are called $true~twins$; (6) A retrograde resonance ($n/Ω< 0$) is always of higher order than its prograde counterpart ($n/Ω> 0$); (7) the resonance strengths can be calculated in a compact form with the classical operators used in the case of a perturbing satellite. Applications to Chariklo and Haumea are made.
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