Abstract
Classical Floquet theory is reviewed with careful attention to the case of repeated eigenvalues common in Hamiltonian systems. Floquet theory generates a canonical transformation to modal variables if the periodic matrix can be made symplectic at the initial time. It is shown that this symplectic normalization can always be carried out, again with careful attention to the degenerate case. The periodic modal vectors and canonical modal variables can always be chosen to be purely real. It is possible to introduce real valued action-angle variables for all modes. Physical interpretation of the canonical degenerate normal modal variables are offered. Finally, it is shown that this transformation enables canonical perturbation theory to be carried out using Floquet modal variables.
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Wiesel, W.E., Pohlen, D.J. Canonical Floquet theory. Celestial Mech Dyn Astr 58, 81–96 (1994). https://doi.org/10.1007/BF00692119
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DOI: https://doi.org/10.1007/BF00692119