A New Superintegrable Hamiltonian

Details A New Superintegrable Hamiltonian A New Superintegrable Hamiltonian

2007-12-21

arxiv.org/abs/0712.3677v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, 4 figures, submitted to The Journal of Mathematical Physics

Scientific paper

10.1063/1.2840465

We identify a new superintegrable Hamiltonian in 3 degrees of freedom, obtained as a reduction of pure Keplerian motion in 6 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 3 degrees of freedom, there are 5 functionally independent integrals of motion, and all bound, classical trajectories are closed and strictly periodic. The generalisation 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.

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