Inspired by this question. Can a 3 body problem, starting with two planets orbit

Question

Inspired by this question. Can a 3 body problem, starting with two planets orbiting a larger one (so massive it may be taken to stand still) in perpendicular planes, be stable?

Is there known an analytical solution to this 3 body problem?
Or a qualitative description of the evolution?
Will the two bodies approach coplanar orbits?

Bounty for this:

Is Classical Mechanics (that is Newtons 1/r^2 law) sufficient for some large random collection of point-particles (with nonzero net angular momentum) in orbit around a larger one, sufficient to explain that they approach coplanar orbits?
Or is it needed to add collisions and energy loss etc..

Explanation / Answer

Poincar

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