Regular Polygon Central Configuration of the Restricted 1 + N-Body Problem-Reference-Cited by-同舟云学术

Regular Polygon Central Configuration of the Restricted 1 + N-Body Problem

Published:2023-05-26 Issue:6 Volume:9 Page:254
ISSN:2218-1997
Container-title:Universe
language:en
Short-container-title:Universe

Author:

Chen Jian¹^ORCID,Bi Peng¹,Yang Mingfang²

Affiliation:

1. School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, China

2. School of Information Engineering, Southwest University of Science and Technology, Mianyang 621010, China

Abstract

We consider the central configurations of the 1+N-body problem, where N bodies are infinitesimal and the remaining one body is dominant. For regular polygon central configurations, we prove that the masses of all the infinitesimal bodies are equal when N is odd and the masses of the alternate infinitesimal bodies must be equal when N is even. Moreover, in the case of N being even, we present the relationship of the mass parameters between two consecutive infinitesimal bodies.

Funder

Natural Science Foundation of Sichuan Province

Natural Science Foundation of Southwest University of Science and Technology

Publisher

MDPI AG

Subject

General Physics and Astronomy

Link

https://www.mdpi.com/2218-1997/9/6/254/pdf

Reference17 articles.

1. Saari, D.G. (2005). Collisions, Rings and Other Newtonian N-Body Problems, AMS.

2. On the role and the properties of n body central configurations;Saari;Celest. Mech. Dyn. Astron.,1980

3. Brush, S., Everitt, C.W.F., and Garber, E. (1983). Maxwell on Saturn’s Rings, MIT Press.

4. Central configurations of the planar 1+n body problem;Casasayas;Celest. Mech. Dyn. Astron.,1994

5. Linear stability of relative equilibria with a dominant mass;Moeckel;J. Dyn. Differ. Equ.,1994