## Sunday, January 29, 2012

### Non-Linear Dynamics, a Redneck Perspective

Non-linear dynamics baffle most sane people. They cause things that don't seem possible to happen. If you have ever had a tire on your car start to separate, you have had some experience with the joys of non-linear dynamics.

Initially, everything feels just fine. Then you notice a slight difference at some speed with maybe an extra passenger in the car or less fuel in the tank. You speed up or slow down it goes away. Then you start to take the car to the mechanic, but it drives just fine, so you put off the visit.

As you are driving down the road to visit grandma out of town, the vibration comes back. You make it to grandma's and check everything out. Nothing looks out of place. After having dinner and some of Granny's apple crisps, you take to car to a mechanic. Without even looking at the car he tells you how much a new set of tires cost. You blow him off, because there is no way that Gomer possibly knows what is wrong with your Beemer.

So you head back to Granny's with the car riding just fine. Heading home in a light rain, the car drives just perfectly. Gomer is a dumbbutt obviously since there is nothing wrong with the car.

The next afternoon, in scorching heat, you hurry back to catch the first half of the big game and your tire blows out on the freeway. Just bad luck that you miss the game waiting on AAA.

The initial conditions in each case caused different responses. Load, speed and temperature change the frequency of the oscillation of the imbalance in the tire.

A tire is a pretty simple example. Climate is not so simple an example but shares similar traits. Weather has pseudo-cyclic oscillations. Those oscillations have an average peak to peak value. A twice peak to peak value tends to be a record of some kind. While records are special, they happen. So a twice peak to peak value in a non-linear dynamic system is rare, but expected. They are actually signatures of non-linear dynamic systems. So if someone believes that a twice peak to peak change is abnormal, they obviously think they are dealing with a linear system. In that case, they need to listen to Gomer :)