论文标题
彗星和月亮解决方案在时间依赖的限制$（n+1）$ - 身体问题
Comet and moon solutions in the time-dependent restricted $(n+1)$-body problem
论文作者
论文摘要
依赖时间的限制$（n+1）$ - 身体问题涉及在$ n $ body问题的定期解决方案后，由$ n $主要身体产生的重力场的影响，对无质量身体（卫星）的研究。我们证明，卫星具有定期的解决方案，接近开普勒问题（彗星溶液）的大振幅圆形轨道，并且在初次处于相对平衡的情况下，接近小振幅的圆形轨道（月球溶液）。彗星和月亮溶液是通过将lyapunov-schmidt还原降低到动作功能的。此外，使用可逆性技术，我们以数值计算超八编舞后四个初选的情况下计算彗星和月球解决方案。
The time-dependent restricted $(n+1)$-body problem concerns the study of a massless body (satellite) under the influence of the gravitational field generated by $n$ primary bodies following a periodic solution of the $n$-body problem. We prove that the satellite has periodic solutions close to the large-amplitude circular orbits of the Kepler problem (comet solutions), and in the case that the primaries are in a relative equilibrium, close to small-amplitude circular orbits near a primary body (moon solutions). The comet and moon solutions are constructed with the application of a Lyapunov-Schmidt reduction to the action functional. In addition, using reversibility technics, we compute numerically the comet and moon solutions for the case of four primaries following the super-eight choreography.
