Using Inönü-Wigner Lie-algebra contraction and a local slice on the cotangent bundle, non-degenerate relative equilibria and relative periodic orbits of general Hamiltonian systems persist from the Euclidean plane to spheres and hyperbolic planes of constant curvature, with application to the n-body
McGehee, Triple collision in the collinear three-body problem, Invent
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Continuation of Hamiltonian dynamics from the plane to constant-curvature surfaces
Using Inönü-Wigner Lie-algebra contraction and a local slice on the cotangent bundle, non-degenerate relative equilibria and relative periodic orbits of general Hamiltonian systems persist from the Euclidean plane to spheres and hyperbolic planes of constant curvature, with application to the n-body