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The double pendulum, a simple system of classical mechanics, is widely studied as an example of, and testbed for, chaotic dynamics. In [1], Maiti et al. study 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 this rotating 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 [2] algorithm for the Dixon resultant [3], written in the computer algebra system (CAS) Fermat [4], to be capable to complete the computation for the challenging system of equations that represents bifurcation, while alternative algorithms or implementations could not be found to complete the computations. This work demonstrates the opportunity that exists if equations of equilibrium and bifurcation can be transformed into polynomial systems, to make use of computational algebra techniques to further analyze these features of dynamical systems. 

rotating double pendulum, Lagrangian mechanics, polynomial resultants, Dixon resultant, DixonEDF, bifurcation of equilibrium solutions.