### 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 language | English (US) |
---|---|

Pages (from-to) | 17-24 |

Number of pages | 8 |

Journal | Celestial Mechanics |

Volume | 28 |

Issue number | 1-2 |

DOIs | |

State | Published - Sep 1 1982 |

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### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Celestial Mechanics*,

*28*(1-2), 17-24. https://doi.org/10.1007/BF01230656

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

Research output: Contribution to journal › Article

*Celestial Mechanics*, vol. 28, no. 1-2, pp. 17-24. https://doi.org/10.1007/BF01230656

}

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 -