  The noncanonical Hamiltonian formulation of magnetohydrodynamics (MHD) is
used to construct variational principles for symmetric equilibrium
configurations of magnetized plasma including flow. In particular, helical
symmetry is considered and results on axial and translational symmetries are
retrieved as special cases of the helical configurations. The symmetry
condition, which allows the description in terms of a magnetic flux function,
is exploited to deduce a symmetric form of the noncanonical Poisson bracket of
MHD. Casimir invariants are then obtained directly from the Poisson bracket.
Equilibria are obtained from an energy-Casimir principle and reduced forms of
this variational principle are obtained by the elimination of algebraic
constraints.
