Are all solutions of the 3-body problem restricted to 2 dimensions? I am not a physicist.
Suppose there are two massive bodies orbiting each other. Their orbit will presumably define a plane.  As far as I know, the existing solutions to the 3-body problem are limited to a plane.
Has any work been done on 3-dimensional orbits? For example two bodies are orbiting one another and a third body enters the system at right angle to their plane?
Specifically (1) Are there any solutions even for special cases of this? (2) Would such 3-D systems inevitability decay into 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.