A New Superintegrable Hamiltonian
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.
Keywords
Cite
@article{arxiv.0712.3677,
title = {A New Superintegrable Hamiltonian},
author = {P. E. Verrier and N. W. Evans},
journal= {arXiv preprint arXiv:0712.3677},
year = {2009}
}
Comments
11 pages, 4 figures, submitted to The Journal of Mathematical Physics