Closedness of orbits in a space with SU(2) Poisson structure

@article{Fatollahi2014ClosednessOO,
  title={Closedness of orbits in a space with SU(2) Poisson structure},
  author={Amir H. Fatollahi and Ahmad Shariati and Mohammad Khorrami},
  journal={arXiv: Classical Physics},
  year={2014}
}
The closedness of orbits of central forces is addressed in a three dimensional space in which the Poisson bracket among the coordinates is that of the SU(2) Lie algebra. In particular it is shown that among problems with spherically symmetric potential energies, it is only the Kepler problem for which all of the bounded orbits are closed. In analogy with the case of the ordinary space, a conserved vector (apart from the angular momentum) is explicitly constructed, which is responsible for the… 

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