How to Calculate the 2 balance points "Swinging Sticks" physics toy/desk sculpture??

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Please, this is something I have thought of a long time, but don't have unlimited supplies to keep doing it wrong. I want to make one of these for my nephew, he's interested in science!

There is a Physics Toy, called "Swinging Sticks", used in the movie "Iron Man 2", on Pepper Pott's desk. How can I calculate the 2 balance points for the "sticks" in this toy, to make it keep spinning a long time? - Here is a great Youtube video of the toy:

https://www.youtube.com/watch?v=DhFHAEQ5x4c