论文标题
与库仑（n+1）的柏拉图polyhedra的对称性的辫子 - 身体问题
Braids with the symmetries of Platonic polyhedra in the Coulomb (N+1)-body problem
论文作者
论文摘要
我们考虑了n = 12、24、60的库仑（n + 1） - 体问题。其中一个粒子具有正电荷q> 0，其余的n具有相同的负电荷q <0。这些颗粒在库仑力下移动，并且假定正电荷在质量中心处于静止状态。由柏拉图多面体的对称组给出的对称约束，我们能够使用射击方法和延续相对于正电荷的值q来计算周期性轨道。 在经典n体问题的设置中，通过最小化动作功能，通过变异技术的计算证明了这种轨道的存在。在这里，这种方法似乎不起作用，数值计算表明我们计算的轨道不是动作的最小化器。
We take into account the Coulomb (N + 1)-body problem with N = 12, 24, 60. One of the particles has positive charge Q > 0, and the remaining N have all the same negative charge q < 0. These particles move under the Coulomb force, and the positive charge is assumed to be at rest at the center of mass. Imposing a symmetry constraint, given by the symmetry group of the Platonic polyhedra, we were able to compute periodic orbits, using a shooting method and continuation with respect to the value Q of the positive charge. In the setting of the classical N -body problem, the existence of such orbits is proved with Calculus of Variation techniques, by minimizing the action functional. Here this approach does not seem to work, and numerical computations show that the orbits we compute are not minimizers of the action.
