Advertisement

Chaos

Chapter
  • 1.8k Downloads
Part of the The Frontiers Collection book series (FRONTCOLL)

Abstract

Oddly, the story of low-dimensional chaos begins with Isaac Newton’s formulation of mathematical laws governing the motions of the planets and moons of the Solar System in his Principia Mathematica which was published in 1687. Based on calculus, which Newton also invented, these laws of motion describe how a massive body responds to forces (friction and gravitational attraction) acting on it. I write “oddly” because the motions of the planets in their elliptic orbits about the Sun — with lines from each planet to the Sun sweeping out equal areas in equal times, in accord with Kepler’s law — seem to be among the most regular phenomena in our experience. The Sun rises every morning at times that were accurately predicted centuries ago, and the positions of the planets against the stellar background have been retrodicted for many centuries into the past, in agreement with earlier observations.

Keywords

Solar System Invariant Torus Planetary Orbit Planetary Motion Lorenz Attractor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Personalised recommendations