Are all solutions of the 3-body problem restricted to 2 dimensions?
Are all solutions of the 3-body problem restricted to 2 dimensions?

The five stationary solutions to the three body problem are restricted to a plane. That does not mean that all solutions are restricted to a plane.

Has any work been done on 3-dimensional orbits?

NASA is proposing to build its Lunar Gateway as a vehicle in a &quot;Near-Rectilinear Halo Orbit&quot; (NRHO) about the Moon. These halo orbits only exist in the presence of a third body, in this case, the Earth. The orbit is nearly orthogonal to the Moon's orbit about the Earth.