## Instability of a whirling conducting rod in the presence
of a magnetic field

G.H.M. van der Heijden & J. Valverde

We study the effect of a magnetic field on the behaviour of a slender
conducting elastic structure subject to end forces. Both statical (buckling)
and dynamical (whirling) instability are considered and we also compute
post-buckling configurations. The theory used is the geometrically exact
Cosserat rod theory. We consider two types of boundary conditions: the
traditional welded boundary conditions and a novel set of boundary conditions
that give rise to exact helical post-buckling solutions. Our results are
relevant for current designs of electrodynamic space tethers and potentially
for future applications in nano- and molecular wires.
keywords: conducting rod, magnetic field, Cosserat theory, bifurcation,
helical solutions, space tether

*Proc. of the 5th EUROMECH Nonlinear Dynamics Conference (ENOC 2005),
7-12 August 2005, Eindhoven, The Netherlands*, D.H. van Campen,
M.D. Lazurko, W.P.J.M. van den Oever (eds), pp. 2624-2633,
ISBN 90-386-2667-3 (2005)