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A method, called beatification, is presented for rapidly extracting weaklynonlinear Hamiltonian systems that describe the dynamics near equilibria forsystems possessing Hamiltonian form in terms of noncanonical Poisson brackets.The procedure applies to systems like fluids and plasmas in terms of Eulerianvariables that have such noncanonical Poisson brackets, i.e., brackets withnonstandard and possibly degenerate form. A collection of examples of bothfinite and infinite dimensions is presented.

Weakly nonlinear dynamics in noncanonical Hamiltonian systems with applications to fluids and plasmas