A first integral to the partially averaged Newtonian potential of the three-body problem

被引：7

作者：

Pinzari, Gabriella ^{[1
]}

机构：

[1] Dipartimento Matemat T Levi Civita, Via Trieste 63, I-35131 Padua, Italy

来源：

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 2019年 / 131卷 / 05期

基金：

欧洲研究理事会;

关键词：

Integrable systems; Renormalizable integrability; Harrington property; Herman resonance; 34C20; 70F10; 37J10; 37J15; 37J40; ARNOLDS THEOREM; STABILITY;

D O I：

10.1007/s10569-019-9899-z

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

We consider the partial average, i.e. the Lagrange average with respect to just one of the two mean anomalies, of the Newtonian part of the perturbing function in the three-body problem Hamiltonian. We prove that such a partial average exhibits a non-trivial first integral. We show that this integral is fully responsible for certain cancellations in the averaged Newtonian potential, including a property noticed by Harrington in the 1960s. We also highlight its joint role (together with certain symmetries) in the appearance of the so-called Herman resonance. Finally, we discuss an application and an open problem.

引用

页数：30

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