平面圆周限制性五体问题的变分最小解

本文对四个等质量和一个零质量的平面牛顿圆周限制性五体问题，通过利用变分的方法，并且通过比较拉格朗日作用函数在测试轨道和碰撞轨道上的上、下界, 证明了一种新的非碰撞周期解的存在性。

Variational minimizing solutions for planar circular restricted 5-body problems

For planar Newtonian circular restricted 5-bodyproblems with 4-equal and one zero primaries, through variationalmethods, we prove the existence of new noncollision periodic solutions. To avoid collisions, we compare the lower bound for the lagrangian action on the symmetry collision orbits and the upper bound for the lagrangian action on the test orbits.