论文标题
在天体力学中有两个自由问题的射血碰撞轨道
Ejection-collision orbits in two degrees of freedom problems in celestial mechanics
论文作者
论文摘要
在具有两个自由度的哈密顿系统的一般环境中，并假定具有潜力的某些特性，我们研究了动力学的关闭，并趋向于系统的奇异性，该系统在$ n $ n $ body问题的模型中与总碰撞相对应。我们仅限于表现出另外两个奇异性的潜力，当并非所有尸体都涉及时，这些奇点可以被视为两种部分碰撞。将奇异性正规化，总碰撞转变为二维不变的歧管。本文的目的是证明存在不同类型的弹出轨道的存在，即在总碰撞时开始和结束的轨道。这样的轨道被认为是两个平衡点之间的杂斜连接，并且主要以轨迹在途中发现的部分碰撞为特征。它们存在的证明是基于二维不变歧管的横向性以及在总碰撞歧管上的动力学行为，它们均得到充分描述。
In a general setting of a Hamiltonian system with two degrees of freedom and assuming some properties for the undergoing potential, we study the dynamics close and tending to a singularity of the system which in models of $N$-body problems corresponds to total collision. We restrict to potentials that exhibit two more singularities that can be regarded as two kind of partial collisions when not all the bodies are involved. Regularizing the singularities, the total collision transforms into a 2-dimensional invariant manifold. The goal of this paper is to prove the existence of different types of ejection-collision orbits, that is, orbits that start and end at total collision. Such orbits are regarded as heteroclinic connections between two equilibrium points and are mainly characterized by the partial collisions that the trajectories find on their way. The proof of their existence is based on the transversality of 2-dimensional invariant manifolds and on the behavior of the dynamics on the total collision manifold, both of them are thoroughly described.
