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?