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Published in:
2012 | OriginalPaper | Chapter
Polygonal RE
Author : Florin Diacu
Published in: Relative Equilibria of the Curved N-Body Problem
Publisher: Atlantis Press
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The goal of this chapter is to study polygonal RE in
$$ {\text{S}}^{ 2} $$
and
$$ {\text{H}}^{ 2} $$
. Since these manifolds are embedded in
$$ {\text{R}}^{ 3} $$
, we will drop the
w
coordinate from now on and use an
xyz
frame. Given the fact that the dimension is reduced by one, we will not encounter positive elliptic-elliptic and negative elliptic-hyperbolic RE anymore. So the only orbits we will deal with from now on are the positive and negative elliptic as well as the negative hyperbolic RE.