Spherical chaos: both arms swing in polar & azimuthal angles
What changed vs. 2D?
The original double pendulum swings inside one flat plane (two angles). This one has
four generalized coordinates — a polar angle θ and azimuthal
angle φ for each arm — so the whole system can precess out of any fixed plane.
The extra freedom is solved from the real 3D rigid-rod Lagrangian (mass matrix + Coriolis
terms), not a fake wobble layered on top of the 2D motion.