Journal of Nonlinear Science

, Volume 20, Issue 3, pp 309-339

First online:

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

  • J. ValverdeAffiliated withDepartment of Civil and Environmental Engineering, University of California
  • , G. H. M. van der HeijdenAffiliated withCentre for Nonlinear Dynamics, University College London Email author 

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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 mechanics Kirchhoff equations Magnetic buckling Degenerate pitchfork bifurcations Hopf bifurcation Spinning electrodynamic tether

Mathematics Subject Classification (2000)

74K10 74G60 78A30 34B15 37L15