Periodic orbits for the planar newtonian three-body problem coming from the elliptic restricted three-body problems

Jaume Llibre; Donald G. Saari

doi:10.1090/S0002-9947-1995-1297534-X

Periodic orbits for the planar newtonian three-body problem coming from the elliptic restricted three-body problems

Jaume Llibre, Donald G. Saari

Department of Mathematics

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

6 Citations (Scopus)

Abstract

Through the introduction of a new coordinate system followed by a Poincaré compactification, a new relationship is developed to connect the planar three-body problem with the various planar restricted three-body systems. This framework is further used to develop new conditions for the continuation of symmetric periodic orbits from elliptic restricted systems to the full planar threebody problem. © 1995 American Mathematical Society.

Original language	English
Pages (from-to)	3017-3030
Journal	Transactions of the American Mathematical Society
Volume	347
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9947-1995-1297534-X
Publication status	Published - 1 Jan 1995

Keywords

Periodic orbits
Restricted problem
Three-body problem

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10.1090/S0002-9947-1995-1297534-X

Cite this

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title = "Periodic orbits for the planar newtonian three-body problem coming from the elliptic restricted three-body problems",

abstract = "Through the introduction of a new coordinate system followed by a Poincar{\'e} compactification, a new relationship is developed to connect the planar three-body problem with the various planar restricted three-body systems. This framework is further used to develop new conditions for the continuation of symmetric periodic orbits from elliptic restricted systems to the full planar threebody problem. {\textcopyright} 1995 American Mathematical Society.",

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AU - Saari, Donald G.

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N2 - Through the introduction of a new coordinate system followed by a Poincaré compactification, a new relationship is developed to connect the planar three-body problem with the various planar restricted three-body systems. This framework is further used to develop new conditions for the continuation of symmetric periodic orbits from elliptic restricted systems to the full planar threebody problem. © 1995 American Mathematical Society.

AB - Through the introduction of a new coordinate system followed by a Poincaré compactification, a new relationship is developed to connect the planar three-body problem with the various planar restricted three-body systems. This framework is further used to develop new conditions for the continuation of symmetric periodic orbits from elliptic restricted systems to the full planar threebody problem. © 1995 American Mathematical Society.

KW - Periodic orbits

KW - Restricted problem

KW - Three-body problem

U2 - 10.1090/S0002-9947-1995-1297534-X

DO - 10.1090/S0002-9947-1995-1297534-X

M3 - Article

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VL - 347

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EP - 3030

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 8

ER -

Periodic orbits for the planar newtonian three-body problem coming from the elliptic restricted three-body problems

Abstract

Keywords

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