We are interested in defining new energy functionals and solving them by
using the variational approach method. That is, we aim to define a new
class of elastic curves in the three-dimensional ordinary space. We
further improve an alternative method to find critical points of the
bending energy functionals acting on a class of magnetic curves. Then,
we classify these critical curves as elastic magnetic curves of the
Frenet-Serret vector family. Moreover, we investigate the dynamics of
the elastic magnetic curves of ferromagnetic and superparamagnetic
models and discuss their numerical and analytical analysis.