Double spherical pendulum synchronization

Simulation of double spherical pendulums initialized to synchronize positions at one time.

Both the planar and spherical double pendulums were simulated with Hamilton's equations of the same Hamiltonian. This Hamiltonian was derived with excessive coordinates, specifically constrained Cartesian coordinates with six degrees of freedom instead of four. Unlike common implementations with angle coordinates, this Hamiltonian is never ill-conditioned and does not generate significant errors (or division by zero) near the poles, and is also more efficient as it does not use trigonometric functions.

The second video section is a playback of the first with slower speed.

The systems were simulated using high order explicit symplectic integrators and was rendered in real time.

[andrenovgorodcev]

Hello, very nice video! I am working with a similar problem, but inside the water and considering external forces caused by vortex induced vibration and damping. I am very curious to see the set of Hamilton's equations that you implemented, mainly to see how you modeled the plane where the pendulums are connected. Is it possible to share the equations?