A New Superintegrable Hamiltonian

P. E. Verrier; N. W. Evans

doi:10.1063/1.2840465

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arXiv · 0712.3677

A New Superintegrable Hamiltonian

P. E. Verrier·N. W. Evans

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Abstract

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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P. E. Verrier, N. W. Evans. 2007-12-21. A New Superintegrable Hamiltonian. https://doi.org/10.1063/1.2840465

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