Kohn's theorem and Newton-Hooke symmetry for Hill's equations
  Hill's equations, which first arose in the study of the Earth-Moon-Sun system, admit the two-parameter centrally extended Newton-Hooke symmetry without rotations. This symmetry allows for extending Kohn's theorem about the center-of-mass decomposition. Particular light is shed on the problem using Duval's "Bargmann" framework. The separation of the center-of-mass motion into that of a guiding center and relative motion is derived by a generalized chiral decomposition. 
P. M. Zhang, G. W. Gibbons, P. A. Horvathy
hep-th astro-ph.GA gr-qc math-ph math.MP