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December 2018 3+1-Moulton configuration
Naoko Yoshimi, Akira Yoshioka
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SUT J. Math. 54(2): 173-190 (December 2018). DOI: 10.55937/sut/1549536790


We pose a new problem of collinear central configuration in Newtonian n-body problem. For a given three-body of collinear central configuration, we ask whether we can add another body in a way such that (a) the total four-body is also in a state of collinear central configuration and (b) the initial three-body keeps its motion without any change during the process. We find four solutions to the above problem having zero mass. We also discuss a similar but ‘positive’ problem by modifying the conditions such that (a) the four-body is in a state of collinear central configuration and the initial three bodies keep their position without any change, and (b) the masses of the two out of the three of initial bodies are invariant with the rest having a slight change and the mass of the added body is positive.

We also find explicit solutions to the second problem.


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Naoko Yoshimi. Akira Yoshioka. "3+1-Moulton configuration." SUT J. Math. 54 (2) 173 - 190, December 2018.


Received: 14 November 2018; Revised: 30 November 2018; Published: December 2018
First available in Project Euclid: 8 June 2022

Digital Object Identifier: 10.55937/sut/1549536790

Primary: 70F10 , 70F15

Keywords: celestial mechanics , Collinear central configuration , four-body problem

Rights: Copyright © 2018 Tokyo University of Science

Vol.54 • No. 2 • December 2018
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