  A method, called beatification, is presented for rapidly extracting weakly
nonlinear Hamiltonian systems that describe the dynamics near equilibria for
systems possessing Hamiltonian form in terms of noncanonical Poisson brackets.
The procedure applies to systems like fluids and plasmas in terms of Eulerian
variables that have such noncanonical Poisson brackets, i.e., brackets with
nonstandard and possibly degenerate form. A collection of examples of both
finite and infinite dimensions is presented.
