论文标题
在受限的三个身体问题中
Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem
论文作者
论文摘要
本文考虑了在多个坐标系统中定义的保守系统的两个点边界价值问题，并为计算机辅助存在证明开发了灵活的A-Posteriori框架。我们的框架适用于研究碰撞和圆形限制的三个身体问题的近碰撞轨道。在这种情况下，坐标系是标准旋转坐标，而两个LEVI-CIVITA坐标系统将碰撞与每个巨大的初选正式碰撞。所提出的框架用于证明存在许多轨道的存在，这些轨道长期以来在天体力学文献中进行了数字研究，但对于此处考虑的质量和能量值没有现有的分析证明。其中包括从一个初级身体到另一个身体的横向弹射/碰撞，Strömgren的cysymptotic周期轨道（用于$ L_ {4,5} $的横向同质轨道），经过碰撞的周期性轨道家族，以及将$ L_4 $ l_4 $ to Extion或Collision连接到$ L_4的轨道。
This paper considers two point boundary value problems for conservative systems defined in multiple coordinate systems, and develops a flexible a-posteriori framework for computer assisted existence proofs. Our framework is applied to the study collision and near collision orbits in the circular restricted three body problem. In this case the coordinate systems are the standard rotating coordinates, and the two Levi-Civita coordinate systems regularizing collisions with each of the massive primaries. The proposed framework is used to prove the existence of a number of orbits which have long been studied numerically in the celestial mechanics literature, but for which there are no existing analytical proofs at the mass and energy values considered here. These include transverse ejection/collisions from one primary body to the other, Strömgren's assymptotic periodic orbits (transverse homoclinics for $L_{4,5}$), families of periodic orbits passing through collision, and orbits connecting $L_4$ to ejection or collision.
