  The problem of constructing internally rotating solitons of fixed angular
frequency $\omega$ in the Faddeev-Skyrme model is reformulated as a variational
problem for an energy-like functional, called pseudoenergy, which depends
parametrically on $\omega$. This problem is solved numerically using a gradient
descent method, without imposing any spatial symmetries on the solitons, and
the dependence of the solitons' energy on $\omega$, and on their conserved
total isospin $J$, studied. It is found that, generically, the shape of a
soliton is independent of $\omega$, and that its size grows monotonically with
$\omega$. A simple elastic rod model of time-dependent hopfions is developed
which, despite having only one free parameter, accounts well for most of the
numerical results.
