To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Variational principle

From Wikipedia, the free encyclopedia

In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those functions. For example, the problem of determining the shape of a hanging chain suspended at both ends—a catenary—can be solved using variational calculus, and in this case, the variational principle is the following: The solution is a function that minimizes the gravitational potential energy of the chain.

Overview

Any physical law which can be expressed as a variational principle describes a self-adjoint operator.[1][verification needed] These expressions are also called Hermitian. Such an expression describes an invariant under a Hermitian transformation.

History

Felix Klein's Erlangen program attempted to identify such invariants under a group of transformations. In what is referred to in physics as Noether's theorem, the Poincaré group of transformations (what is now called a gauge group) for general relativity defines symmetries under a group of transformations which depend on a variational principle, or action principle.

Examples

In mathematics

In physics

References

  1. ^ Lanczos, Cornelius (1974) [1st published 1970, University of Toronto Press]. The Variational Principles of Mechanics (4th, paperback ed.). Dover. p. 351. ISBN 0-8020-1743-6.
  • Ekeland, Ivar (1979). "Nonconvex minimization problems". Bulletin of the American Mathematical Society. New Series. 1 (3): 443–474. doi:10.1090/S0273-0979-1979-14595-6. MR 0526967.
  • S T Epstein 1974 "The Variation Method in Quantum Chemistry". (New York: Academic)
  • R.P. Feynman, "The Principle of Least Action", an almost verbatim lecture transcript in Volume 2, Chapter 19 of The Feynman Lectures on Physics, Addison-Wesley, 1965. An introduction in Feynman's inimitable style.
  • C Lanczos, The Variational Principles of Mechanics (Dover Publications)
  • R K Nesbet 2003 "Variational Principles and Methods In Theoretical Physics and Chemistry". (New York: Cambridge U.P.)
  • S K Adhikari 1998 "Variational Principles for the Numerical Solution of Scattering Problems". (New York: Wiley)
  • C G Gray, G Karl G and V A Novikov 1996, Ann. Phys. 251 1.
  • C.G. Gray, G. Karl, and V. A. Novikov, "Progress in Classical and Quantum Variational Principles". 11 December 2003. physics/0312071 Classical Physics.
  • Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-805326-X.
  • John Venables, "The Variational Principle and some applications". Dept of Physics and Astronomy, Arizona State University, Tempe, Arizona (Graduate Course: Quantum Physics)
  • Andrew James Williamson, "The Variational Principle -- Quantum monte carlo calculations of electronic excitations". Robinson College, Cambridge, Theory of Condensed Matter Group, Cavendish Laboratory. September 1996. (dissertation of Doctor of Philosophy)
  • Kiyohisa Tokunaga, "Variational Principle for Electromagnetic Field". Total Integral for Electromagnetic Canonical Action, Part Two, Relativistic Canonical Theory of Electromagnetics, Chapter VI
  • Komkov, Vadim (1986) Variational principles of continuum mechanics with engineering applications. Vol. 1. Critical points theory. Mathematics and its Applications, 24. D. Reidel Publishing Co., Dordrecht.
  • Cassel, Kevin W.: Variational Methods with Applications in Science and Engineering, Cambridge University Press, 2013.
This page was last edited on 20 August 2021, at 09:12
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.