论文标题
靠近拉格朗日解决方案的过渡$ l_1，l_2 $在椭圆限制的三体问题中
Transits close to the Lagrangian solutions $L_1,L_2$ in the Elliptic Restricted Three-body Problem
论文作者
论文摘要
在过去的几十年中，圆形限制的三个身体问题的奇特解决方案已被用来解释太阳系的行星对小体和航天器的临时捕获。这些解决方案已使用近似局部积分和jacobi常数的值对lagrangian点$ l_1，l_2 $ l_2 $ l_2 $ l_2 $进行了交通。太阳系小体的使用需要考虑从CRTBP到整个$ n $行星问题的模型的层次扩展。椭圆形限制的三个体是CRTBP的第一个自然扩展，这已经代表了一个挑战，因为诸如雅各比常数之类的全球第一积分（例如，雅各比常数）并非以此问题而闻名。在本文中，我们使用Floquet理论和Birkhoff正常化的组合扩展了靠近Lagrangian点$ L_1，L_2 $ L_2 $的分类。只要满足某些非共振条件，我们将问题的哈密顿量与余数结合到了可综合的正常形式的哈密顿式形式，该形式用于定义近似局部的第一积分，并根据这些积分的值来通过lagrange平衡的邻里进行分类。我们为Earth-Moon Ertbp提供数值演示。
In the last decades a peculiar family of solutions of the Circular Restricted Three Body Problem has been used to explain the temporary captures of small bodies and spacecrafts by a planet of the Solar System. These solutions, which transit close to the Lagrangian points $L_1,L_2$ of the CRTBP, have been classified using the values of approximate local integrals and of the Jacobi constant. The use for small bodies of the Solar System requires to consider a hierarchical extension of the model, from the CRTBP to the the full $N$ planetary problem. The Elliptic Restricted Three Body, which is the first natural extension of the CRTBP, represents already a challenge, since global first integrals such as the Jacobi constant are not known for this problem. In this paper we extend the classification of the transits occurring close to the Lagrangian points $L_1,L_2$ of the ERTBP using a combination of the Floquet theory and Birkhoff normalizations. Provided that certain non-resonance conditions are satisfied, we conjugate the Hamiltonian of the problem to an integrable normal form Hamiltonian with remainder, which is used to define approximate local first integrals and to classify the transits of orbits through a neighbourhood of the Lagrange equilibria according to the values of these integrals. We provide numerical demonstrations for the Earth-Moon ERTBP.
