  We study the effect of a magnetic field on the behaviour of a slender
conducting elastic structure, motivated by stability problems of electrodynamic
space tethers. Both statical (buckling) and dynamical (whirling) instability
are considered and we also compute post-buckling configurations. The equations
used are the geometrically exact Kirchhoff equations. Magnetic buckling of a
welded rod is found to be described by a surprisingly degenerate bifurcation,
which is unfolded when both transverse anisotropy of the rod and angular
velocity are considered. By solving the linearised equations about the (quasi-)
stationary solutions we find various secondary instabilities. Our results are
relevant for current designs of electrodynamic space tethers and potentially
for future applications in nano- and molecular wires.
