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New Orbits for the n ‐Body Problem
Author(s) -
VANDERBEI ROBERT J.
Publication year - 2004
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1196/annals.1311.024
Subject(s) - action (physics) , three body problem , n body problem , mathematics , stability (learning theory) , periodic orbits , computer science , physics , classical mechanics , mathematical analysis , quantum mechanics , machine learning
A bstract : 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.