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

TL;DR

This paper demonstrates that the combined effects of extensibility and a magnetic field make the equations governing a conducting rod nonintegrable, leading to spatial chaos, which impacts electrodynamic space tethers and electromechanical devices.

Contribution

It shows that while individual effects preserve integrability, their combination destroys it, revealing complex chaotic behavior in conducting rods under magnetic influence.

Findings

Combined effects lead to nonintegrability and chaos.

Magnetic field influences the stability of conducting rods.

Implications for space tethers and electromechanical systems.

Abstract

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.