The inverse problem for collinear central configurations

Alain Albouy; Richard Moeckel

doi:10.1023/A:1008345830461

The inverse problem for collinear central configurations

Alain Albouy
, Richard Moeckel

School of Mathematics

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

We consider the problem: given a collinear configuration of n bodies, find the masses which make it central. We prove that for n ≤ 6, each configuration determines a one-parameter family of masses (after normalization of the total mass). The parameter is the center of mass when n is even and the square of the angular velocity of the corresponding circular periodic orbit when n is odd. The result is expected to be true for any n.

Original language	English (US)
Pages (from-to)	77-91
Number of pages	15
Journal	Celestial Mechanics and Dynamical Astronomy
Volume	77
Issue number	2
DOIs	https://doi.org/10.1023/A:1008345830461
State	Published - 2000

Keywords

Central configuration
Inverse problem
n-body problem

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10.1023/A:1008345830461

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title = "The inverse problem for collinear central configurations",

abstract = "We consider the problem: given a collinear configuration of n bodies, find the masses which make it central. We prove that for n ≤ 6, each configuration determines a one-parameter family of masses (after normalization of the total mass). The parameter is the center of mass when n is even and the square of the angular velocity of the corresponding circular periodic orbit when n is odd. The result is expected to be true for any n.",

keywords = "Central configuration, Inverse problem, n-body problem",

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T1 - The inverse problem for collinear central configurations

AU - Albouy, Alain

AU - Moeckel, Richard

PY - 2000

Y1 - 2000

N2 - We consider the problem: given a collinear configuration of n bodies, find the masses which make it central. We prove that for n ≤ 6, each configuration determines a one-parameter family of masses (after normalization of the total mass). The parameter is the center of mass when n is even and the square of the angular velocity of the corresponding circular periodic orbit when n is odd. The result is expected to be true for any n.

AB - We consider the problem: given a collinear configuration of n bodies, find the masses which make it central. We prove that for n ≤ 6, each configuration determines a one-parameter family of masses (after normalization of the total mass). The parameter is the center of mass when n is even and the square of the angular velocity of the corresponding circular periodic orbit when n is odd. The result is expected to be true for any n.

KW - Central configuration

KW - Inverse problem

KW - n-body problem

UR - https://www.scopus.com/pages/publications/0042227650

UR - https://www.scopus.com/pages/publications/0042227650#tab=citedBy

U2 - 10.1023/A:1008345830461

DO - 10.1023/A:1008345830461

M3 - Article

AN - SCOPUS:0042227650

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EP - 91

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

IS - 2

ER -

The inverse problem for collinear central configurations

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