  The equations for strands of rigid charge configurations interacting
nonlocally are formulated on the special Euclidean group, SE(3), which
naturally generates helical conformations. Helical stationary shapes are found
by minimizing the energy for rigid charge configurations positioned along an
infinitely long molecule with charges that are off-axis. The classical energy
landscape for such a molecule is complex with a large number of energy minima,
even when limited to helical shapes. The question of linear stability and
selection of stationary shapes is studied using an SE(3) method that naturally
accounts for the helical geometry. We investigate the linear stability of a
general helical polymer that possesses torque-inducing non-local
self-interactions and find the exact dispersion relation for the stability of
the helical shapes with an arbitrary interaction potential. We explicitly
determine the linearization operators and compute the numerical stability for
the particular example of a linear polymer comprising a flexible rod with a
repeated configuration of two equal and opposite off-axis charges, thereby
showing that even in this simple case the non-local terms can induce
instability that leads to the rod assuming helical shapes.
