  The double pendulum, a simple system of classical mechanics, is widely
studied as an example of, and testbed for, chaotic dynamics. In 2016, Maiti et
al. studied a generalization of the simple double pendulum with equal
point-masses at equal lengths, to a rotating double pendulum, fixed to a
coordinate system uniformly rotating about the vertical. In this paper, we
study a considerable generalization of the double pendulum, constructed from
physical pendula, and ask what equilibrium configurations exist for the system
across a comparatively large parameter space, as well as what bifurcations
occur in those equilibria. Elimination algorithms are employed to reduce
systems of polynomial equations, which allows for equilibria to be visualized,
and also to demonstrate which models within the parameter space exhibit
bifurcation. We find the DixonEDF algorithm for the Dixon resultant, written in
the computer algebra system (CAS) Fermat, to be capable to complete the
computation for the challenging system of equations that represents
bifurcation, while attempts with other algorithms were terminated after several
hours.
