Translator Disclaimer
VOL. 22 | 2021 $4 + 1$-Moulton Configuration and Positive Mass Deformation
Naoko Yoshimi, Akira Yoshiok

Editor(s) Ivaïlo M. Mladenov, Vladimir Pulov, Akira Yoshioka

Abstract

For given $k$ bodies of collinear central configuration of Newtonian $k$-body problem, we ask whether one can add another body on the line without changing the configuration and motion of the initial bodies so that the total $k + 1$ bodies provide a central configuration.

The case $k = 4$ is analyzed. We study the inverse problem of five bodies and obtain a global explicit formula. Then using the formula we find there are five possible positions of the added body and for each case the mass of the added body is zero. We further consider to deform the position of the added body without changing the positions of the initial four bodies so that the total five bodies are in a state of central configuration and the mass of the added body becomes positive. For each solution above, we find such a deformation of the position of the added body in an explicit manner starting from the solution.

Information

Published: 1 January 2021
First available in Project Euclid: 2 June 2021

Digital Object Identifier: 10.7546/giq-22-2021-286-300

Rights: Copyright © 2021 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

PROCEEDINGS ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
RIGHTS & PERMISSIONS
Get copyright permission
Back to Top