论文标题
$ n $ body问题的可正常线性周期性解决方案与任意群众
Regularizable collinear periodic solutions in the $n$-body problem with arbitrary masses
论文作者
论文摘要
对于有任意正质量的$ n $ body问题，我们证明有可正常的共线周期性解决方案用于任何群体的订购，从同时二进制碰撞到另一个时期的另一个群体，其中一半的群体单调向右边单调移动，另一半则单调地向左单图。当群众满足某些平等条件时，解决方案会具有额外的对称性。当$ n = 3 $时，这也提供了Schubart Orbit存在的新证明。
For $n$-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the masses moving monotonically to the right and the other half monotonically to the left. When the masses satisfy certain equality condition, the solutions have extra symmetry. This also gives a new proof of the existence of Schubart orbit, when $n=3$.
