Embrace chaos by making your own double pendulum fidget spinner

If the novelty of holding an elaborate bearing (possibly connected to some motion-sensitive LEDs) is wearing thin, have no fear: with a 3D printer and a little ingenuity, you can make your own double-pendulum fidget spinner, a chaotic system that is intensely sensitive to initial conditions, such that it becomes very hard to predict the motion of the pendulum when you set it to swinging.

What's more, replacing the pendulums' strings with springs produces an even more satisfyingly chaotic motion, as Rhett Allain demonstrates in his Wired column on the devices, which includes editable mathematical simulations that let you play with the parameters (this is admittedly not as fun as the pendulum would likely be).

What if I replaced the strings in the double pendulum with springs? How many degrees of freedom would the system have now? Each mass could still swing back and forth so that would be two angles (and two degrees of freedom) but the springs could also move towards or away from the attachment points (two more degrees of freedom). This gives a total of four degrees of freedom. If the double pendulum is difficult to model, the double spring pendulum must be nearly impossible. Right?

Nope. It's easier.

Consider the bottom mass (mass 2) in this spring pendulum thingy. There are essentially two forces acting on this mass. There is the gravitational force pulling down, which depends on the mass of the object and the gravitational field, and then there is the force from the spring. Both of these forces are deterministic forces—meaning you can calculate both their magnitude and direction at any instant. The spring force depends on the stiffness of the spring and the location of the two masses. Once I have the total force acting on mass 2, I can use the momentum principle to find how its momentum changes. With the momentum of mass 2, I can find out where it is after some short time interval. This the basic recipe of a numerical calculation—I don't have to use Lagrangian mechanics to find the motion. It's perfect for a computer to calculate.


Double Pendulum Fidget Spinner [BrittLiv/Instructables]