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Comet and Moon Solutions in the Time-Dependent Restricted $$(n+1)$$ ( n + 1 ) -Body Problem
Journal of Dynamics and Differential Equations ( IF 1.3 ) Pub Date : 2021-01-11 , DOI: 10.1007/s10884-020-09929-1
Carlos Barrera , Abimael Bengochea , Carlos García-Azpeitia

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 techniques, we compute numerically the comet and moon solutions for the case of four primaries following the super-eight choreography.



中文翻译:

时间相关受限$$(n + 1)$$(n + 1)-身体问题中的彗星和月球解决方案

随时间变化的受限制的\(((n + 1)\)-体)问题涉及在n个周期的周期解之后n初级体产生的引力场影响下的无质量体(卫星)的研究。身体问题。我们证明了卫星具有接近开普勒问题的大振幅圆轨道的周期解(彗星解),并且在原边处于相对平衡的情况下,接近于主体附近的小振幅圆轨道(月球解决方案)。彗星和月球解决方案是通过将Lyapunov–Schmidt归约应用于动作功能而构造的。此外,使用可逆性技术,我们根据超八种编排方法,针对四个原色的情况,通过数值计算彗星和月球解。

更新日期:2021-01-11
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