EPS 102 lecture 18

# EPS 102 lecture 18 - EPS 102 Lecture 18 Tuesday March 31st,...

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EPS 102 Lecture 18 Tuesday March 31 st , 2009 Chaos and Chaotic Systems: Chaos is when physically or mathematically simple systems can show really complicated behavior. One example (about the orbits of the planets) is that when you consider multiple planets, the gravitational interactions between them lead to chaotic motions; occasionally fragments are ejected out of the asteroid belts and those become meteorites or asteroids that intersect with our planet. Chaos is also interesting because we don’t really understand it. About 10 years ago the British government celebrated the millennium with the construction of a footbridge over the River Thames in London. On opening day the bridge started to wobble from side to side. Lock in is a phenomenon like ex: if you swing your legs on a swing quickly and randomly nothing happens but if you swing them at the right motion, you set up a pendulum motion. You can amplify by reinforcing. Chaos: Simple system that can show surprisingly complex behavior characterized by multiple dynamic states, (where motions can be very different from each other and has many different kinds of motions possible. On a swing, one kind of motion is back and forth but high enough, the swing can go all the way over the pole = back and forth up to circular. On the bridge, we went from small vibrations to the actual amplified swing because people were stepping along to the swings to reinforce it) the ability to switch between these states (could be periodic switching or no switching at all), can oscillated between different states periodically, when in a chaotic motions, the actual motion of the system is exponentially sensitive to the initial conditions or constraints (if you try to reproduce the same process, it is impossible because the tiniest difference between starting states will give very different final states). 2 different solutions to the same

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## This note was uploaded on 02/04/2010 for the course EPS 102 taught by Professor Staff during the Spring '08 term at Berkeley.

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EPS 102 lecture 18 - EPS 102 Lecture 18 Tuesday March 31st,...

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