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

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Abstract

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.

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Correspondence to G. H. M. van der Heijden.

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Communicated by A.R. Champneys.

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Valverde, J., van der Heijden, G.H.M. Magnetically-Induced Buckling of a Whirling Conducting Rod with Applications to Electrodynamic Space Tethers. J Nonlinear Sci 20, 309–339 (2010). https://doi.org/10.1007/s00332-010-9059-9

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  • DOI: https://doi.org/10.1007/s00332-010-9059-9

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