  The equilibrium of magneto-elastic rods, formed of an elastic matrix
containing a uniform distribution of paramagnetic particles, that are subject
to terminal loads and are immersed in a uniform magnetic field, is studied. The
deduced nonlinear equilibrium equations are fully consistent with Kirchhoff's
theory in the sense that they hold at the same order of magnitude. Exact
solutions of those equations in terms of Weierstrass elliptic functions are
presented with reference to magneto-elastic cantilevers that undergo planar
deformations under the action of a terminal force and a magnetic field whose
directions are either parallel or orthogonal. The exact solutions are applied
to the study of a problem of remotely controlled deformation of a rod and to a
bifurcation problem in which the end force and the magnetic field act as an
imperfection parameter and a bifurcation parameter, respectively.
