论文标题
周期性不平等质量轨道的Broucke-Hadjidemetriou-Hénon家族的卫星
Satellites of the Broucke-Hadjidemetriou-Hénon family of periodic unequal-mass three-body orbits
论文作者
论文摘要
Broucke-Hadjidemetriou-hénon（BHH）轨道是具有最简单的拓扑免费组单词$ a $ a $的三体系统的周期性轨道家族，而BHH卫星具有免费的组单词$ a^k $（$ k> 1 $），其中$ k $是拓扑指数。 Janković和Dmitrašinović[Phy。莱特牧师。 116，064301（2016）]报告了57个新的BHH卫星，并发现在固定能量下，角动量（$ L $）与拓扑上的重新分组（$ t/k $）之间的关系对于BHH Orbits（$ k = 1 $）和BHH卫星（BHH卫星（BHH）卫星（$ k = 1 $）都是相同的。在这封信中，我们报告了419,743个新的BHH轨道（$ k = 1 $）和179,253个新的BHH卫星（$ k> 1 $）的三体系统中，据我们所知，这是从未有过不平等质量的三体系统。在这些新发现的598,996个BBH轨道和卫星中，大约33.5％（即200,686）是线性稳定的，因此在实践中可能会观察到其中许多。此外，我们发现，对于具有固定能量的三体系统而言，BHH卫星（$ k> 1 $）的角动量（$ l $）和拓扑恢复时期（$ t/k $）之间的关系与BHH Orbits（$ k> 1 $）不同。
The Broucke-Hadjidemetriou-Hénon's (BHH) orbits are a family of periodic orbits of the three-body system with the simplest topological free group word $a$, while the BHH satellites have free group words $a^k$ ($k>1$), where $k$ is the topological exponent. Janković and Dmitrašinović [Phy. Rev. Lett. 116, 064301 (2016)] reported 57 new BHH satellites with equal mass and found that at a fixed energy the relationship between the angular momentum ($L$) and the topologically rescaled period ($T/k$) is the same for both of the BHH orbits ($k=1$) and the BHH satellites ($k>1$). In this letter, we report 419,743 new BHH orbits ($k=1$) and 179,253 new BHH satellites ($k>1$) of the three-body system with unequal mass, which have never been reported, to the best of our knowledge. Among these newly-found 598,996 BBH orbits and satellites, about 33.5 % (i.e., 200,686) are linearly stable and thus many among them might be observed in practice. Besides, we discover that, for the three-body system with unequal mass at a fixed energy, relationship between the angular momentum ($L$) and topologically rescaled period ($T/k$) of the BHH satellites ($k>1$) is different from that of the BHH orbits ($k=1$).
