Finiteness of relative equilibria in the planar generalized N-body problem with fixed subconfigurations

Marshall Hampton; Anders Nedergaard Jensen

doi:10.3934/jgm.2015.7.35

Finiteness of relative equilibria in the planar generalized N-body problem with fixed subconfigurations

Marshall Hampton, Anders Nedergaard Jensen

Mathematics & Statistics

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

7 Scopus citations

Abstract

We prove that a fixed configuration of N - 1 masses in the plane can be extended to a central configuration of N masses by adding a specified additional mass only in finitely many ways. This holds for a family of potential functions including the Newtonian gravitational case and the classical planar point vortex model.

Original language	English (US)
Pages (from-to)	35-42
Number of pages	8
Journal	Journal of Geometric Mechanics
Volume	7
Issue number	1
DOIs	https://doi.org/10.3934/jgm.2015.7.35
State	Published - Mar 1 2015

Bibliographical note

Publisher Copyright:
© American Institute of Mathematical Sciences

Keywords

Celestial mechanics
Central configurations
N-body problem
Relative equilibria
Vortices

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10.3934/jgm.2015.7.35

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abstract = "We prove that a fixed configuration of N - 1 masses in the plane can be extended to a central configuration of N masses by adding a specified additional mass only in finitely many ways. This holds for a family of potential functions including the Newtonian gravitational case and the classical planar point vortex model.",

keywords = "Celestial mechanics, Central configurations, N-body problem, Relative equilibria, Vortices",

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KW - Relative equilibria

KW - Vortices

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Finiteness of relative equilibria in the planar generalized N-body problem with fixed subconfigurations

Abstract

Bibliographical note

Keywords

Publisher link

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