Action minimizing orbits in the 2+2- and 3+2-body problems with 2 fixed centers

In the Newtonian 2+2-body problem with two fixed centers in R3, two particles with equal masses are assumed fixed and the trajectories of the remaining 2 particle with equal masses interact and are affected by the two fixed particles according to Newton’s second law and the Universal law. We show th...

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Bibliographic Details
Published inJournal of geometry and physics Vol. 149; p. 103578
Main Authors Zhao, Furong, Jiang, Yueyong
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2020
Subjects
2+2-body problems with 2 fixed centers
3+2-body problems with 2 fixed centers
Circular solutions
Newtonian potentials
Variational minimization
34C15
70F10
2+2-body problems with 2 fixed centers
34C25
3+2-body problems with 2 fixed centers
Newtonian potentials
Circular solutions
Variational minimization
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Summary:In the Newtonian 2+2-body problem with two fixed centers in R3, two particles with equal masses are assumed fixed and the trajectories of the remaining 2 particle with equal masses interact and are affected by the two fixed particles according to Newton’s second law and the Universal law. We show that the minimization of the action functional on suitable classes of loops yields collision-free periodic orbits of the 2+2-body problem ; more precisely, geometric information is obtained for such variational minimization solutions. For the Newtonian 3+2-body problem with two fixed centers in R3, similar results are obtained.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2019.103578