Hamiltonian formulation of ferromagnetic hydrodynamics

Darryl D. Holm, Boris A. Kupershmidt
1988 Physics Letters A  
The equations of ideal ferromagnetic hydrodynamics (FMHD) in three dimensions are formulated as a hamiltonian system in terms of a noncanonical Poisson bracket. The conservation laws for this system are determined and used to construct Lyapunov functionals that are potentially useful for dealing with stability properties of FMHD equilibrium solutions. Classes of equilibrium solutions are identified with critical points of these Lyapunov functionals. The FMHD system is also formulated in n
more » ... ions and the relations among magnetic induction, magnetic field intensity, and magnetization density are discussed from a Lie-algebraic viewpoint.
doi:10.1016/0375-9601(88)90076-x fatcat:zos5zkh3nfbv7cnbvrbb7yf4mi