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The Theory of Oscillations. The Variational Principle (Continued)

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

Abstract

Thus the kinetic and potential energies of the string (Fig. 7.1) have the form \( T = \frac{1} {2}\int\limits_0^l {\dot u^2 dx,U = \frac{k} {2}\int\limits_0^l {(u_x )^2 dx} }\).

Keywords

Potential Energy Riemannian Manifold Quadratic Form Variational Principle Volume Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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