A new superintegrable Hamiltonian

We identify a new superintegrable Hamiltonian in three degrees of freedom, obtained as a reduction of pure Keplerian motion in six dimensions. The new Hamiltonian is a generalization of the Keplerian one, and has the familiar 1 ∕ r potential with three barrier terms preventing the particle crossing the principal planes. In three degrees of freedom, there are five functionally independent integrals of motion, and all bound, classical trajectories are closed and strictly periodic. The generalization of the Laplace–Runge–Lenz vector is identified and shown to provide functionally independent isolating integrals. They are quartic in the momenta and do not arise from separability of the Hamilton–Jacobi equation. A formulation of the system in action-angle variables is presented.