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.
keywords: elastic rod, magnetostatics, Hamiltonian mechanics, integrability, homoclinic orbits, Melnikov analysis, horseshoe dynamicsJournal of Physics A: Mathematical and Theoretical 44, 495101 (2011)