论文标题
超越平面循环限制的三体问题的牛顿动力学与Kerr样初选
Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries
论文作者
论文摘要
研究了在纽顿超越近似的背景下，平面循环限制的三体问题的动力学与Kerr样原则。通过使用Fodor-Hoenselaers-Perjés程序，开发了牛顿的超越潜力。进行KERR电位的扩展，并包括质量和自旋效应的第一个非牛顿贡献的术语。有了这一潜力，研究了两个初选的赤道平面中无限质量质量的测试粒子的模型。引入一个参数$ε$，可以检查系统从牛顿过渡到牛顿超越政权的过程。还研究了系统固定点随参数$ε$的函数的演变和稳定性。使用poincaré截面图和最大lyapunov指数作为混乱的指标研究粒子的动力学。对于两种主要质量比例（$ = 0.001,0.5 $）的情况，$ε$的中间值似乎是最混乱的。系统中的混乱数量仍高于牛顿系统，以及对于所有非零值$ε$的平面循环限制的三体问题。
The dynamics of the planar circular restricted three-body problem with Kerr-like primaries in the context of a beyond-Newtonian approximation is studied. The beyond-Newtonian potential is developed by using the Fodor-Hoenselaers-Perjés procedure. An expansion in the Kerr potential is performed and terms up-to the first non-Newtonian contribution of both the mass and spin effects are included. With this potential, a model for a test particle of infinitesimal mass orbiting in the equatorial plane of the two primaries is examined. The introduction of a parameter, $ε$, allows examination of the system as it transitions from the Newtonian to the beyond-Newtonian regime. The evolution and stability of the fixed points of the system as a function of the parameter $ε$ is also studied. The dynamics of the particle is studied using the Poincaré map of section and the Maximal Lyapunov Exponent as indicators of chaos. Intermediate values of $ε$ seem to be the most chaotic for the two cases of primary mass-ratios ($=0.001,0.5$) examined. The amount of chaos in the system remains higher than the Newtonian system as well as for the planar circular restricted three-body problem with Schwarzschild-like primaries for all non-zero values of $ε$.
