Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set
Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set
复制标题
DOI：
10.1007/s10569-019-9890-8
复制
发表时间：
2018-08
影响因子：
1.6
通讯作者：
Shane Kepley;J. M. Mireles James
中科院分区：
文献类型：
--
作者：
Shane Kepley;J. M. Mireles James
我们描述了一种方法来计算一个图集的稳定或不稳定的流形连接到一个平衡点和实现的方法的鞍焦点平动点的平面等边限制四体问题。我们采用的方法在最大对称的情况下，质量相等，在那里我们计算的稳定和不稳定的流形的地图集。由此产生的地图集由数千个单独的图表地图组成，每个图表由一个双变量泰勒多项式表示。后处理的图集数据产生近似的不变流形的交叉点，我们通过一个适当的两点边值问题的射击方法来完善。最后，我们将数值延拓应用于一些边值问题。这打破了对称性，并导致连接轨道的一些不平等的价值观的主要质量。
We describe a method for computing an atlas for the stable or unstable manifold attached to an equilibrium point and implement the method for the saddle-focus libration points of the planar equilateral restricted four-body problem. We employ the method at the maximally symmetric case of equal masses, where we compute atlases for both the stable and unstable manifolds. The resulting atlases are comprised of thousands of individual chart maps, with each chart represented by a two-variable Taylor polynomial. Post-processing the atlas data yields approximate intersections of the invariant manifolds, which we refine via a shooting method for an appropriate two-point boundary value problem. Finally, we apply numerical continuation to some of the BVP problems. This breaks the symmetries and leads to connecting orbits for some nonequal values of the primary masses.