  A Hamiltonian and action principle formalism for deriving three-dimensional
gyroviscous magnetohydrodynamic models is presented. The uniqueness of the
approach in constructing the gyroviscous tensor from first principles and its
ability to explain the origin of the gyromap and the gyroviscous terms are
highlighted. The procedure allows for the specification of free functions,
which can be used to generate a wide range of gyroviscous models. Through the
process of reduction, the noncanonical Hamiltonian bracket is obtained and
briefly analysed.
