X-Sieve: CMU Sieve 2 - Edwin F. Taylor



email:

19 January 2004

Dear Andrew: Attached is the WORD file EFTWebsiteChange0104C.doc and a couple of new pdf files. Two more pdf files are attached to the following message.

Love, Dad

19 January 2004

Andrew Taylor

Webmaster to the Stars

Dear Andrew:

Here is my memory of our plans for the Principle of Least Action page(s) of the website.

1. Delete all POSTED dates.

2. Delete some existing items:

DELETE: Quick derivation

DELETE: Simple example:

DELETE: Comparative example

DELETE: Introductory physics text, already in its second edition.

Also DELETE the descriptor words that start each item: Preprint or Derivation etc.

3. Two columns side by side. Left column: a shortened introduction and a few pdf downloads. Right column: a (boxed?) list of articles with titles, authors, and references but no descriptions. When the operator clicks on an article s/he is taken to a fuller description of that article on a separate page, from which it can be downloaded.

Here is the shortened introduction in the left-hand column, which starts with the quote that was formerly boxed. THERE IS ONE SMALL CHANGE IN THE FOLLOWING QUOTE. Some of the pdf files are new, some are ones already installed on the website. "Existing" includes those added Monday 1/19.

LEFT-HAND COLUMN

[FOLLOWING IS A QUOTE, in italics]

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.

[END OF QUOTE]

The principle of least action has wide applicability in undergraduate physics education, from mechanics in introductory classes through electricity and magnetism, quantum mechanics, special and general relativity—and it provides a deep foundation for advanced subjects and current research.

INTERACTIVE SOFTWARE

Principle of Least Action Interactive (zip archive of all files or on-line JAVA applications) by Slavomir Tuleja and Edwin F. Taylor. An interactive introduction to the Principle of Least Action. Twenty-six questions for the student to answer using five different JAVA interactive displays. If you are having trouble running the JAVA applets, read the readme file (pdf format)

EXISTING TEXT

"The Lagrange Method" by David Morin, a chapter on the Lagrange equations derived from the principle of least action, from a draft honors introductory physics text. Many problems and solutions. Download from Harvard (pdf format)

**THIS IS THE SAME AS EARLIER ITEM: DRAFT: THE LAGRANGE EQUATIONS UNDER EXISTING TEXTBOOKS

ANNOTATED BIBLIOGRAPHY

The principle of least action and Lagrange's equations were introduced one century after Newton's great work. The bibliography (pdf format) lists books that describe this history and apply the results. Full references, ISBNs, and excerpts.

**USE EXISTING FILE

RIGHT-HAND COLUMN

[The RIGHT-hand column will have title, authors, and reference. Clicking on the article will take the reader to a list of articles that repeats the reference and adds brief descriptions, from which a pdf file can be downloaded.]

ARTICLES LISTED IN THE RIGHT-HAND COLUMN (BOX?)

ARTICLES

"A Call to Action," Edwin F. Taylor. Guest Editorial, Am. J. Phys., Vol. 71, No. 5, May 2003, pages 423-425.

"Deriving the nonrelativistic principle of least action from the Schwarzschild metric and the principle of maximal aging," Edwin F. Taylor.

"From conservation of energy to the principle of least action: A story line," Jozef Hanc and Edwin F. Taylor. Accepted Am. J. Phys.

"Simple derivation of Newtonian mechanics from the principle of least action," Jozef Hanc, Slavomir Tuleja, Martina Hancova. Am. J. Phys., Vol. 71. No. 4, April 2003, pages 386 - 391.

"Deriving Lagrange's equations using elementary calculus," Jozef Hanc, Edwin F. Taylor, and Slavomir Tuleja. Accepted Am. J. Phys.

"Symmetries and Conservation Laws: Consequences of Noether's Theorem" Jozef Hanc, Slavomir Tuleja, and Martina Hancova. Accepted Am. J. Phys.

"The original Euler's calculus-of-variations method: Key to Lagrangian mechanics for beginners," Jozef Hanc. Submitted to Eur. J. Phys.

"Getting the most action out of least action: A proposal," Thomas A. Moore. Accepted Am. J. Phys.

FULLER DESCRIPTIONS OF ARTICLES ON A SEPARATE PAGE TO WHICH USER IS TAKEN WHEN S/HE CLICKS ON ARTICLE IN RIGHT-HAND COLUMN OF FIRST PAGE. ATTACHED TO THIS MESSAGE (AND MAYBE LATER MESSAGES) ARE THE NEW FILES:

FmaAJPguest5.pdf

GRtoPLA2.pdf

ActionFINAL.pdf

Symmetry0104.pdf

"A Call to Action," Edwin F. Taylor. Guest Editorial, American Journal of Physics Vol. 71, No. 5, May 2003, pages 423-425. Outlines the case for using the principle of least action to begin mechanics in introductory physics classes.

**USE NEW FILE: FmaAJPguest5.pdf

"Deriving the nonrelativistic principle of least action from the Schwarzschild metric and the principle of maximal aging," Edwin F. Taylor. Unpublished appendix to the guest editorial "A Call to Action." Demonstrates that the principle of least action is a limiting case of general relativity for the motion of a free particle external to a spherically symmetric, nonrotating center of gravitational attraction.

**USE NEW FILE: GRtoPLA2.pdf

"From conservation of energy to the principle of least action: A story line," Jozef Hanc and Edwin F. Taylor. Accepted Am. J. Phys. Proposes that the study of Newtonian mechanics begin with the conservation of energy, the use of constraints and constants of the motion to simplify the analysis of motion, and a heuristic transition to the principle of least action and Lagrange's equations.

**USE EXISTING FILE

"Simple derivation of Newtonian mechanics from the principle of least action," Jozef Hanc, Slavomir Tuleja, Martina Hancova. American Journal of Physics, Vol. 71. No. 4, April 2003, pages 386 - 391. Derives Newton's laws of motion from the principle of least action.

**USE NEW FILE (ActionFINAL.pdf)

"Deriving Lagrange's equations using elementary calculus," Jozef Hanc, Edwin F. Taylor, and Slavomir Tuleja. Accepted Am. J. Phys. Lagrange's equations, alternatives to F=ma, are usually derived from the principle of least action using the calculus of variations. This paper derives them using elementary calculus.

**USE EXISTING FILE

"Symmetries and Conservation Laws: Consequences of Noether's Theorem" Jozef Hanc, Slavomir Tuleja, and Martina Hancova. Accepted Am. J. Phys. The extremely powerful Noether's Theorem allows one to derive conservation laws from the symmetries of the action that describes the motion of a system.

**USE NEW FILE (Symmetry0104.pdf)

"The original Euler's calculus-of-variations method: Key to Lagrangian mechanics for beginners," Jozef Hanc. Submitted to Eur. J. Phys.

Euler's original version of the calculus of variations was geometric and easily visualized. Instead, Euler adopted Lagrange's elegant algebraic method which still dominates our advanced mechanics classrooms. Recently Euler's method has been resurrected, shown to be rigorous and more general than Lagrange's, and employed in computer solutions of physical processes. The geometric and easily visualized Euler's method can now be applied to almost all of undergraduate physics.

**USE EXISTING FILE

"Getting the most action out of least action: A proposal," Thomas A. Moore. Accepted Am. J. Phys. Examines the potential advantages of using the principle of least action in advanced undergraduate classes, including simpler and deeper introductions to intermediate mechanics, relativity, electricity and magnetism, and quantum mechanics and some contemporary topics.

**USE EXISTING FILE

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