Open Access
2018 2+1-Moulton Configuration
Naoko Yoshimi, Akira Yoshioka
J. Geom. Symmetry Phys. 50: 79-95 (2018). DOI: 10.7546/jgsp-50-2018-79-95


We pose a new problem of collinear central configuration in Newtonian $n$-body problem. For a given two-body, we ask whether we can add a new body in a way such that i) the configuration of the total three-body is also collinear central with the configuration of the initial two-body being fixed and further ii) the initial two-body keeps its motion without any change during the process. We find three solutions to the above problem. We also consider a similar problem such that while the condition i) is satisfied but by modifying the condition ii) the motion of the initial two-body is not necessarily equal to the original one. We also find explicit solutions to the second problem.


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Naoko Yoshimi. Akira Yoshioka. "2+1-Moulton Configuration." J. Geom. Symmetry Phys. 50 79 - 95, 2018.


Published: 2018
First available in Project Euclid: 26 January 2019

zbMATH: 07063862
MathSciNet: MR3929487
Digital Object Identifier: 10.7546/jgsp-50-2018-79-95

Rights: Copyright © 2018 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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