Abstract
In this chapter we will provide examples of negative RE, one for each type of orbit of this kind: elliptic, hyperbolic, and elliptic-hyperbolic. The first is the Lagrangian RE of equal masses, which is a negative elliptic RE of the 3-body problem in \( {\text{H}}^{ 3} \), the second is the Eulerian orbit of equal masses, which is a negative hyperbolic RE of the 3-body problem in \( {\text{H}}^{ 3} \), and the third is an elliptic-hyperbolic orbit that combines the previous two examples in the sense that it inherits their rotations.
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© 2012 Florin Diacu
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Diacu, F. (2012). Negative RE. In: Relative Equilibria of the Curved N-Body Problem. Atlantis Series in Dynamical Systems, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-91216-68-8_11
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DOI: https://doi.org/10.2991/978-94-91216-68-8_11
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Publisher Name: Atlantis Press, Paris
Print ISBN: 978-94-91216-67-1
Online ISBN: 978-94-91216-68-8
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