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arXiv · 1112.4793

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

P. M. Zhang·G. W. Gibbons·P. A. Horvathy
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Abstract

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.

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P. M. Zhang, G. W. Gibbons, P. A. Horvathy. 2012-02-24. Kohn's theorem and Newton-Hooke symmetry for Hill's equations. https://doi.org/10.1103/physrevd.85.045031

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