Affiliation:
1. School of Mathematics and System Sciences , Beihang University , Beijing 100191 , P. R. China
2. Department of Mathematics , Brigham Young University , Provo , UT 84602 , USA
Abstract
Abstract
By applying our variational method, we show that there exist 24 local action minimizers connecting two prescribed configurations: a collinear configuration and a double isosceles configuration in
H
1
(
[
0
,
1
]
,
χ
)
{H^{1}([0,1],\chi)}
in the planar equal-mass four-body problem. Among the 24 local action minimizers, we prove that the one with the smallest action has no collision singularity and it can be extended to a periodic or quasi-periodic orbit. Furthermore, if all the 24 local action minimizers are free of collision, we show that they can generate sixteen different periodic orbits.
Funder
National Natural Science Foundation of China
Subject
General Mathematics,Statistical and Nonlinear Physics
Cited by
5 articles.
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