pendula without rods

so what happens if we build a multi-pendulum with structures other than rigid rods? using hoops (solid tori) is especially mesmerizing, and leads one to believe that the dynamics is very different that the rigid-rod case…

a triple pendulum of rings…or is it?

a more careful analysis would show that using rings is equivalent to using rods, as long as you are careful about the equivalent mass (becuase of moment of inertia, the mass of the solid rod and that of the corresponding ring are not the same).

of course, this is be taken to foolish extremes. i do not recommend that you build the following system:

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