The model I have for ENSO is a Mathieu equation for sloshing, which is analogous to the inverted pendulum on a moving cart experiment. As long as the cart shows a specific back-and-forth oscillation (or an up-and-down -- see below), the pendulum can stably invert.

So check out this cool video related to the inverted pendulum on a cart -- the "rolling" inverted pendulum. Last year Brian Josephson made a YouTube video where he demonstrates how the inverted pendulum property manifested itself in his kitchen !

No wonder he won a Nobel prize -- he is just a plainly intellectually curious fellow.

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This is the up-and-down cyclically forced inverted pendulum

Again, it uses a Mathieu formulation as described in the video summary:

>"This inverted pendulum was realized by only oscillating its pivot in 58Hz. It can be done without feedback control.

You can find the principle explained in some textbooks about non-linear dynamics. This equation of motion is classfied as Mathieu equation. By solving this equation, you can find the stable condition to keep an inverted pendulum upright.

See also WikiPedia, which has short description about how it works;

http://en.wikipedia.org/wiki/Inverted_pendulum"

To many people, this looks counter-intuitive because they can't imagine what keeps the rod upright.

So check out this cool video related to the inverted pendulum on a cart -- the "rolling" inverted pendulum. Last year Brian Josephson made a YouTube video where he demonstrates how the inverted pendulum property manifested itself in his kitchen !

No wonder he won a Nobel prize -- he is just a plainly intellectually curious fellow.

---

This is the up-and-down cyclically forced inverted pendulum

Again, it uses a Mathieu formulation as described in the video summary:

>"This inverted pendulum was realized by only oscillating its pivot in 58Hz. It can be done without feedback control.

You can find the principle explained in some textbooks about non-linear dynamics. This equation of motion is classfied as Mathieu equation. By solving this equation, you can find the stable condition to keep an inverted pendulum upright.

See also WikiPedia, which has short description about how it works;

http://en.wikipedia.org/wiki/Inverted_pendulum"

To many people, this looks counter-intuitive because they can't imagine what keeps the rod upright.