The Theory of Oscillations. The Variational Principle (Continued)

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


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


Potential Energy Riemannian Manifold Quadratic Form Variational Principle Volume Element 
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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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