Gravitational orbits within the 2-body problem can be visualized as conics on the surface of a double cone. Is it reasonable to imagine that 3-body systems can be visualized as quadrics on the surface of a double (or perhaps triple) hypercone? Furthermore, is it reasonable to extend this idea of orbits in n-body systems as being quadrics on the surface of some number of even higher dimensional hypercones?
If this idea isn't complete nonsense, would it be useful computationally?
There is no closed form solution to the n-body problem, and most n-body orbits are non-repeating, so perhaps that means that they cannot be described with quadrics.
There's a 2013 paper titled Conic Sections Beyond $\mathbb{R}^{2}$ which talks about quadrics, but it's purely in the geometric sense.
If this is better suited for the physics stackexchange, I'd be happy to delete this and ask there.