Action-minimizing orbits in the parallelogram four-body problem with equal masses

被引:60
作者
Chen, KC [1 ]
机构
[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA
关键词
D O I
10.1007/s002050100146
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we prove the existence of a new periodic solution for the planar Newtonian four-body problem with equal masses. On this orbit two mass points travel on one star-shaped closed curve while the other two travel on another and have the opposite orientation. The configuration of the masses changes from square to collinear periodically and remains a parallelogram for all time. Our proof is based on a variational approach inspired by a recent work of CHENCINER & MONTGOMERY [5]. By choosing an appropriate subspace of the Sobolev space H-1 ([0, T], V), where V is the configuration space, we show that the action functional restricted to this subspace attains its infimum and any minimizer solves the Newtonian four-body problem. The orbits we found are indeed extensions of these minimizers. By studying the behavior of minimizers in reduced configuration space and comparing their action with rhomboid motions, we show that these minimizers do not experience any collision.
引用
收藏
页码:293 / 318
页数:26
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