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Chaos in a generalized Euler’s three-body problem
Classical and Quantum Gravity ( IF 3.5 ) Pub Date : 2021-08-27 , DOI: 10.1088/1361-6382/ac1be7
Takahisa Igata

Euler’s three-body problem is the problem of solving for the motion of a particle moving in a Newtonian potential generated by two point sources fixed in space. This system is integrable in the Liouville sense. We consider the Euler problem with the inverse-square potential, which can be seen as a natural generalization of the three-body problem to higher-dimensional Newtonian theory. We identify a family of stable stationary orbits in the generalized Euler problem. These orbits guarantee the existence of stable bound orbits. Applying the Poincar map method to these orbits, we show that stable bound chaotic orbits appear. As a result, we conclude that the generalized Euler problem is nonintegrable.



中文翻译:

广义欧拉三体问题中的混沌

欧拉三体问题是求解在牛顿势中运动的粒子的运动问题,该运动由两个固定在空间中的点源产生。该系统在刘维尔意义上是可集成的。我们考虑具有平方反比势的欧拉问题,这可以看作是三体问题对高维牛顿理论的自然推广。我们在广义欧拉问题中确定了一系列稳定的静止轨道。这些轨道保证了稳定束缚轨道的存在。将庞加莱映射方法应用于这些轨道,我们表明出现了稳定的束缚混沌轨道。因此,我们得出结论,广义欧拉问题是不可积的。

更新日期:2021-08-27
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