  The equilibrium equations for an isotropic Kirchhoff rod are known to be
completely integrable. It is also known that neither the effects of
extensibility and shearability nor the effects of a uniform magnetic field
individually break integrability. Here we show, by means of a Melnikov-type
analysis, that, when combined, these effects do break integrability giving rise
to spatially chaotic configurations of the rod. A previous analysis of the
problem suffered from the presence of an Euler-angle singularity. Our analysis
provides an example of how in a system with such a singularity a Melnikov-type
technique can be applied by introducing an artificial unfolding parameter. This
technique can be applied to more general problems.
