  A general procedure for constructing action principles for continuum models
via a generalization of Hamilton's principle of mechanics is described. Through
the procedure, an action principle for a gyroviscous magnetohydrodynamics (MHD)
model is constructed. The model is shown to agree with a reduced version of
Braginskii's fluid equations. The construction reveals the origin of the
gyromap, a device used to derive previous gyrofluid models. Also, a systematic
reduction procedure is presented for obtaining the Hamiltonian structure in
terms of the noncanonical Poisson bracket. The construction procedure yields a
class of Casimir invariants, which are then used to variational principles for
equilibrium equations with flow and gyroviscosity. The procedure for obtaining
reduced fluid models with gyroviscosity is also described.
