Collinear relative equilibria of the planar N-body problem

Julian I Palmore

Research output: Contribution to journalArticle

Abstract

The following theorem is proved. THEOREM. For any n≥2, the set of collinear relative equilibria classes of the n-body problem generates by analytical continuation a total of n!(n+3)/2 relative equilibria classes of the n+1 body problem. Together with Arenstorf's results we state a general theorem for the 4 body problem with 3 arbitrary masses and 1 inferior mass.

Original languageEnglish (US)
Pages (from-to)17-24
Number of pages8
JournalCelestial Mechanics
Volume28
Issue number1-2
DOIs
StatePublished - Sep 1 1982

Fingerprint

many body problem
theorems

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Collinear relative equilibria of the planar N-body problem. / Palmore, Julian I.

In: Celestial Mechanics, Vol. 28, No. 1-2, 01.09.1982, p. 17-24.

Research output: Contribution to journalArticle

Palmore, Julian I. / Collinear relative equilibria of the planar N-body problem. In: Celestial Mechanics. 1982 ; Vol. 28, No. 1-2. pp. 17-24.
@article{86ed99c9172142809b403040bddf8fba,
title = "Collinear relative equilibria of the planar N-body problem",
abstract = "The following theorem is proved. THEOREM. For any n≥2, the set of collinear relative equilibria classes of the n-body problem generates by analytical continuation a total of n!(n+3)/2 relative equilibria classes of the n+1 body problem. Together with Arenstorf's results we state a general theorem for the 4 body problem with 3 arbitrary masses and 1 inferior mass.",
author = "Palmore, {Julian I}",
year = "1982",
month = "9",
day = "1",
doi = "10.1007/BF01230656",
language = "English (US)",
volume = "28",
pages = "17--24",
journal = "Celestial Mechanics and Dynamical Astronomy",
issn = "0923-2958",
publisher = "Springer Netherlands",
number = "1-2",

}

TY - JOUR

T1 - Collinear relative equilibria of the planar N-body problem

AU - Palmore, Julian I

PY - 1982/9/1

Y1 - 1982/9/1

N2 - The following theorem is proved. THEOREM. For any n≥2, the set of collinear relative equilibria classes of the n-body problem generates by analytical continuation a total of n!(n+3)/2 relative equilibria classes of the n+1 body problem. Together with Arenstorf's results we state a general theorem for the 4 body problem with 3 arbitrary masses and 1 inferior mass.

AB - The following theorem is proved. THEOREM. For any n≥2, the set of collinear relative equilibria classes of the n-body problem generates by analytical continuation a total of n!(n+3)/2 relative equilibria classes of the n+1 body problem. Together with Arenstorf's results we state a general theorem for the 4 body problem with 3 arbitrary masses and 1 inferior mass.

UR - http://www.scopus.com/inward/record.url?scp=0345780505&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345780505&partnerID=8YFLogxK

U2 - 10.1007/BF01230656

DO - 10.1007/BF01230656

M3 - Article

VL - 28

SP - 17

EP - 24

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 1-2

ER -