New orbits for the n-body problem

Robert J. Vanderbei

doi:10.1196/annals.1311.024

New orbits for the n-body problem

Robert J. Vanderbei

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

15 Scopus citations

Abstract

In this paper, we consider minimizing the action functional as a method for numerically discovering periodic solutions to the n-body problem. With this method, we can find a large number of choreographies and other more general solutions. We show that most of the solutions found, including all but one of the choreographies, are unstable. It appears to be much easier to find unstable solutions to the n-body problem than stable ones. Simpler solutions are more likely to be stable than exotic ones.

Original language	English (US)
Pages (from-to)	422-433
Number of pages	12
Journal	Annals of the New York Academy of Sciences
Volume	1017
DOIs	https://doi.org/10.1196/annals.1311.024
State	Published - 2004

All Science Journal Classification (ASJC) codes

General Biochemistry, Genetics and Molecular Biology
General Neuroscience
History and Philosophy of Science

Keywords

Action principle
New orbits
n-body problem

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10.1196/annals.1311.024

Cite this

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AB - In this paper, we consider minimizing the action functional as a method for numerically discovering periodic solutions to the n-body problem. With this method, we can find a large number of choreographies and other more general solutions. We show that most of the solutions found, including all but one of the choreographies, are unstable. It appears to be much easier to find unstable solutions to the n-body problem than stable ones. Simpler solutions are more likely to be stable than exotic ones.

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KW - n-body problem

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JO - Annals of the New York Academy of Sciences

JF - Annals of the New York Academy of Sciences

ER -

New orbits for the n-body problem

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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