Journal of Nonlinear Science

, Volume 20, Issue 3, pp 309–339

Magnetically-Induced Buckling of a Whirling Conducting Rod with Applications to Electrodynamic Space Tethers


DOI: 10.1007/s00332-010-9059-9

Cite this article as:
Valverde, J. & van der Heijden, G.H.M. J Nonlinear Sci (2010) 20: 309. doi:10.1007/s00332-010-9059-9


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.


Rod mechanicsKirchhoff equationsMagnetic bucklingDegenerate pitchfork bifurcationsHopf bifurcationSpinning electrodynamic tether

Mathematics Subject Classification (2000)


Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of CaliforniaBerkeleyUSA
  2. 2.Centre for Nonlinear DynamicsUniversity College LondonLondonUK