Abstract
We show how to transform a large class of infinite degree-of-freedom Hamiltonian systems into normal form. The energy-Casimir method that is widely used for ascertaining stability in Hamiltonian fluid and plasma systems is only the first step. A complete description involves changing to coordinates in which the energy is diagonal. This amounts to a transformation to action-angle variables. Because fluid and plasma systems typically have a continuous eigenspectrum, this transformation is nontrivial. It will be shown that a family of integral transforms, which is a generalization of the Hilbert transform, yields action-angle variables for a large class of fluid and plasma systems.
In memory of Pedro Ripa 1946–2001
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Morrison, P.J. (2003). Hamiltonian Description of Fluid and Plasma Systems with Continuous Spectra. In: Velasco Fuentes, O.U., Sheinbaum, J., Ochoa, J. (eds) Nonlinear Processes in Geophysical Fluid Dynamics. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0074-1_4
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DOI: https://doi.org/10.1007/978-94-010-0074-1_4
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