The Lissajous transformation II. Normalization

@article{Deprit1991TheLT,
  title={The Lissajous transformation II. Normalization},
  author={A. Deprit and Antonio Elipe},
  journal={Celestial Mechanics and Dynamical Astronomy},
  year={1991},
  volume={51},
  pages={227-250}
}
  • A. Deprit, A. Elipe
  • Published 1 September 1991
  • Physics, Mathematics
  • Celestial Mechanics and Dynamical Astronomy
Normalization of a perturbed elliptic oscillator, when executed in Lissajous variables, amounts to averaging over the elliptic anomaly. The reduced Lissajous variables constitute a system of cylindrical coordinates over the orbital spheres of constant energy, but the pole-like singularities are removed by reverting to the subjacent Hopf coordinates. The two-parameter coupling that is a polynomial of degree four admitting the symmetries of the square is studied in detail. It is shown that the… 
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