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Where would I set the origin? In the case of the original double pendulum, the origin was set at axis of rotation of the first pendulum. Should I keep using that as my origin? Or maybe use the double pendulum's center of mass?

For the original double pendulum problem, only the linear kinetic energy is considered. In the case of a free flying double pendulum, would you consider rotational kinetic energy as well? Would I be considering the rotational energy about the individual pendulums center of mass or the rotational energy of the pendulums about the systems center of mass?

If my understanding of how to approach this problem is so far off the mark that answering these questions doesn't actually help find the solution, please let me know. And hopefully provide a little insight on where to begin.

Thanks,

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