  The Landau-Lifshitz-Gilbert equation for rigid and saturated ferromagnets is
derived using a two-continuum model constructed by H.F. Tiersten for elastic
and saturated ferromagnets. The relevant basic laws of physics are applied
systematically to the two continua or their combination. The exchange
interaction is introduced into the model through surface distributed magnetic
couples. This leads to a continuum theory with magnetization gradients in the
stored energy density. The saturation condition of the magnetization functions
as constraints on the energy density and has implications in the constitutive
relations.
