Satellites of the BrouckeHadjidemetriouHénon family of periodic unequalmass threebody orbits
Abstract
The BrouckeHadjidemetriouHénon's (BHH) orbits are a family of periodic orbits of the threebody 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 threebody system with unequal mass, which have never been reported, to the best of our knowledge. Among these newlyfound 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 threebody 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 ($k=1$).
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2008.13550
 Bibcode:
 2020arXiv200813550L
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 5 pages, 3 figures