Magnetically-induced buckling of a whirling conducting
rod with applications to electrodynamic space tethers
J. Valverde & G.H.M. van der Heijden
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 static (buckling) and dynamic (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.
keywords: rod mechanics, Kirchhoff equations, magnetic buckling, degenerate
pitchfork bifurcations, Hopf bifurcation, spinning electrodynamic tether
Journal of Nonlinear Science (in the press)