The ordinary pendulum with a weight hanging from a thread is a classic in physics but
it is a bit boring. The forces are easy to analyze and even though they lead to a differential equation
d2α/dt2 ∝ sin(α) that can not be solved by elementary functions the motion is still so predictable it could put you to sleep.
A double pendulum is more than twice as interesting. It moves in complex and mysterious ways and it will
take you into a world of chaotic motion and non-linear phenomena.
The best way to appreciate this is to build your own pendulum. Possible materials are wood or plexiglass.
The ball bearings, axes and the counterweight on the inner arm are attached with superglue.
To strengthen the suspension of the arms it could be wise to have extra blocks to lengthen the holes for the axes.
The outer arm has an adjustable weight. Different positions will result in different behaviour.
Theoretical analysis of the pendulum's movement is best done by starting from the Lagrangian of the system
which leads to a system of ordinary differential equations that can be handled numerically with Runge-Kuttas method.
My first simulation was written in Java which is a bit tricky (but possible) to run in a browser nowadays.
Some code from the latest standard of JS will not work in microsoft's browser so I recommend using a big screen, PC and
Google chrome since that is what I used when I wrote my code.