We provide a novel action principle for nonrelativistic ideal
magnetohydrodynamics in the Eulerian scheme exploiting a Clebsch-type
parametrisation. Both Lagrangian and Hamiltonian formulations have been
considered. Within the Hamiltonian framework, two complementary approaches have
been discussed using Dirac's constraint analysis. In one case the Hamiltonian
is canonical involving only physical variables but the brackets have a
noncanonical structure, while the other retains the canonical structure of
brackets by enlarging the phase space. The special case of incompressible
magnetohydrodynamics is also considered where, again, both the approaches are
discussed in the Hamiltonian framework. The conservation of the stress tensor
reveals interesting aspects of the theory.Comment: 20 pages, LaTeX, a new section on incompressible MHD included,
published in Eur. Phys. J.
