固定三中心的四体问题的三叶型周期解

On Trilobal Periodic Solutions to Four-Body Problem with 3 Fixed Centers

研究在强力势的条件下,分别固定三个等质量的天体在一个正三角形的三个顶点上,其余一个天体在这三个天体所确定的平面上绕这三个天体运动的四体问题的三叶型非碰撞周期解的存在性问题.通过引进La-grange泛函和Palais对称性原理及变分方法的基本理论,证明了四体问题的三叶型非碰撞周期解的存在性.

In this paper,the 4-body problem with strong force potentials is to be discussed,where 3 bodies with the same mass are fixed at the vertices of a regular polygon,and the 4th body winds around the others.By introducing Lagrangian function and using Palais＇ symmetry principle,by using variational minimizing methods,the existence of the non-collision periodic solutions with some winding numbers is proved.