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A full analysis of magnetization reversal of a uniformly magnetized body by coherent rotation is presented. The magnetic energy of the body in the presence of an applied field H is modeled as E=(μ0/2)MT DM-μ0HTM, where T denotes a matrix transpose. This model includes shape anisotropy, any number of uniaxial anisotropies, and any energy that can be represented by an effective field that is a linear function of the uniform magnetization M. The model is a generalization to three dimensions of the Stoner-Wohlfarth model. Lagrange multiplier analysis leads to quadratically convergent iterative algorithms for computation of switching field, coercive field, and the stable magnetization(s) of the body in the presence of any applied field. Magnetization dynamics are examined as the applied field magnitude |H| approaches the switching field Hs, and it is found that the precession frequency f∝(Hs-|H|)(14)/ and the susceptibility χ∝(Hs-|H|)-(12)/.