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