The Theory of Oscillations. The Variational Principle

  • Vladimir I. Arnold
Part of the Universitext book series (UTX)


It is an experimental fact well-known to physicists that the laws of nature can be described by variational principles. The absence of rational grounds for this fact has generated attempts to interpret it theologically, philosophically, and in other ways, as, for example, in the writings of Voltaire, Maupertuis and others in the collection Variational Principles of Mechanics.


Potential Energy Quadratic Form Variational Principle Configuration Space Small Oscillation 
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  1. 1.
    Arnold, V.I.: Mathematical Methods of Classical Mechanics, 2nd edition. Springer, New York (1989)CrossRefGoogle Scholar
  2. 2.
    Klein, F.: Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert. Chelsea, New York (1964)Google Scholar
  3. 3.
    Arnold, V.I.: Ordinary Differential Equations. Springer, Berlin (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
    • 2
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.CEREMADEUniversité de Paris-DauphineParis Cedex 16France

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