Negative RE

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.