New Orbits for the n-Body Problem

Details New Orbits for the n-Body Problem New Orbits for the n-Body Problem

2003-03-07

arxiv.org/abs/astro-ph/0303153v1

Astronomy and Astrophysics

Astrophysics

16 pages, 2 tables, 6 figures

Scientific paper

10.1196/annals.1311.024

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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