We have calculated the total Lagrangian and Rayleigh dissipation functions for an isolated domain of arbitrary cross section in an infinite plate with perpendicular anisotropy. Variation of these functions yields a set of coupled equations describing the motion of the center of mass and the boundaryR(&phgr;) (in general noncircular) of the domain. We neglectzdependence and assume&dgr;/R≪1where &dgr; is the wall ``thickness''. The theory is applicable for applied field variations of arbitrary speed and magnitude. For uniform field pulses, the equations reduce to the Callen‐Josephs theory in the weak‐pulse limit. For pulses >2&pgr;Ms/&agr;, where &agr; is the Gilbert parameter, the behavior again tends to be linear with, generally, a greatly reduced apparent mobility, while in the transition region 2&pgr;Ms&agr;<Hp<2&pgr;Ms/&agr;, the predicted behavior is highly nonlinear with an oscillatory substructure which causes an alternating sequence of collapse‐noncollapse regions in the conventional plot of inverse pulse length vs pulse height. Translatory motion of the domain in a field gradient is also highly nonlinear reducing to ``effective mass'' behavior only whenR H′≪4&pgr;M&agr;. An approximate prediction of the theory is that regardless of the magnitude of the pulse gradient (i) the net displacement is given byx0≈&mgr;WR(dH/dx)t0, where &mgr;Wis the wall mobility and (ii) the minimum elapsed time for a displacement is ≈ &tgr;A=(Ms/2K)(R2/&dgr;2)(&ggr;&agr;)−1, whereKis the anisotropy constant and &ggr; the gyromagnetic ratio. Finally, the theory predicts a finite displacement in a directiontransverseto the sense of the field gradient.