## Spatial chaos of an extensible conducting rod in a uniform magnetic field

D. Sinden & G.H.M. van der Heijden

The 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,
remarkably, 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.
keywords: elastic rod, magnetostatics, Hamiltonian mechanics, integrability,
Melnikov analysis, chaotic behaviour, multipulse homoclinic orbits

*Journal of Physics A: Mathematical and Theoretical* **42**,
375207 (2009)