D Sinden and G H M van der Heijden 2009 J. Phys. A: Math. Theor. 42 375207 doi:10.1088/1751-8113/42/37/375207
Spatial chaos of an extensible conducting rod in a uniform magnetic field
D Sinden and G H M van der Heijden
Show affiliationsThe equilibrium equations for the isotropic Kirchhoff rod are known to form an integrable system. It is also known that the effects of extensibility and shearability of the rod do not break the integrable structure. Nor, as we have shown in a previous paper does the effect of a magnetic field on a conducting rod. Here we show, by means of Mel'nikov analysis, that, interestingly, the combined effects do destroy integrability; that is, the governing equations for an extensible current-carrying rod in a uniform magnetic field are nonintegrable. This result has implications for possible configurations of electrodynamic space tethers and may be relevant for electromechanical devices.
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Issue 37 (18 September 2009)
Received 8 May 2009, in final form 1 August 2009
Published 28 August 2009
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Spatial chaos of an extensible conducting rod in a uniform magnetic field
D Sinden and G H M van der Heijden 2009 J. Phys. A: Math. Theor. 42 375207
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