1112.4793 (P. M. Zhang et al.)

Kohn's theorem and Newton-Hooke symmetry for Hill's equations    [PDF]

P. M. Zhang, G. W. Gibbons, P. A. Horvathy

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.

View original: http://arxiv.org/abs/1112.4793