Monday, November 07, 2005

Principal of Least Action

Edwin F. Taylor

The least-action principle is an assertion about the nature of motion that provides an alternative approach to mechanics completely independent of Newton's laws. Not only does the least-action principle offer a means of formulating classical mechanics that is more flexible and powerful than Newtonian mechanics, [but also] variations on the least-action principle have proved useful in general relativity theory, quantum field theory, and particle physics. As a result, this principle lies at the core of much of contemporary theoretical physics.
Thomas A. Moore "Least-Action Principle" in Macmillan Encyclopedia of Physics, John Rigden, editor, Simon & Schuster Macmillan, 1996, Volume 2, page 840.

Java programming by Slavomir Tuleja
Text by Edwin F. Taylor and Slavomir Tuleja
Draft of March 12, 2003

Here L is called the Lagrangian. In simple cases the Lagrangian is equal to the difference between the kinetic energy T and the potential energy V, that is, L = T – V. In this interactive document we will approximate a continuous worldline with a worldline made of straight connected segments. The computer then multiplies the value of (T – V) on each segment by the time lapse t for that segment and adds up the result for all segments, giving us an approximate value for the action S along the entire worldline. Our task is then to move the connected segments of the worldline so that they result in the minimum total value of the action S.

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