Magnetically-induced buckling of a whirling conducting rod with applications to electrodynamic space tethers

摘要

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