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.

PRINCIPLE OF LEAST ACTION INTERACTIVE
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.