Has to do with chaos theory. Personally i dont buy chaos theory. Im a determinist, so i believe that the dynamics of a double pendulum are such that wild combinations appear from a seemingly simple dynamic although the real dynamics of a dub pendulum are complex
however not impossible to control. i can't embed videos at the moment but there is double inverted pendulum completely stabilized that i will try and find later. pretty bad ass control theory if you ask me
my senior year of college I took a class on this. Finite element analysis. You can determine the forces, movement and acceleration using complex equations derived from the simplest basics. Better love matrixes! But a double pendulum is one of the most simplest examples. Real world applications involve such examples as a car or motorcycle. Which can be viewed as a simple 1D problem (suspension), all the was to a 5D problem (suspension, tire flex, frame flex, seat springs and human body flex) all the way to infinite dimensions. VERY interesting yet VERY challenging.
as a mechanical engineer myself(junior year), i have never seen anything like this. obviously there is alot of dynamics in this like angular accel or velocity, there isent even kinetic or potential enrgey in the system right?? but i think this will never make it anywhere... maybe in an oil rig or somthing that has a big strucure to hold it to be able to do this amont of work to a larger body. its not like some day this type of energy will be able to power cars or skate boards or even refridgerators, just not practicle i dont think, prove me wrong i would love to see something come out of this. really i would. thanks for showing this to me it was interesting