Localisation of a twisted conducting rod in a uniform magnetic field: the Hamiltonian-Hopf-Hopf bifurcation

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

We study localised (multi-pulse homoclinic) post-buckling solutions for an extensible conducting rod under end loads and placed in a uniform magnetic field. The homoclinic bifurcation behaviour is found to be organised by a codimension-two Hamiltonian-Hopf-Hopf bifurcation. We predict new stability results for twisted magnetic rods which are relevant for electrodynamic space tethers and potentially for conducting nanowires in future electromechanical devices.

keywords: elastic rod, magnetic field, multi-pulse homoclinic orbits, Hopf bifurcation

Proc. of the 7th European Nonlinear Dynamics Conference (ENOC 2011), 24-29 July 2011, Rome, Italy, D. Bernardini, G. Rega, F. Romeo (eds) (Department of Structural and Geotechnical Engineering, Sapienza University of Rome, 2011), 2 pages, ISBN 978-88-906234-2-4