We study the localised buckling of an extensible conducting rod subjected
to end loads and placed in a uniform magnetic field. The trivial straight
but twisted rod is described by a non-hyperbolic periodic solution of a
ten-dimensional system of equilibrium equations previously shown to be
nonintegrable and to have chaotic dynamics. Post-buckling solutions,
described by (multi-pulse) homoclinic orbits to the trivial solution, are
computed using new numerical methods designed for the non-hyperbolic case.
We find the bifurcation behaviour of these homoclinic orbits to be organised
by a codimension-two Hamiltonian-Hopf-Hopf bifurcation and predict new
stability results for twisted magnetic rods as dimensionaless end-load and
magnetic-field parameters are varied. Our results are relevant for
electrodynamic space tethers and potentially for conducting nanowires in
future electromechanical devices.
keywords: Cosserat rod theory, magnetically-induced buckling, homoclinic solutions, shooting method, numerical continuation, Hopf bifurcation, elastic stability, space tethersubmitted to Physica D