The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations

Released on by Ian Anderson
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  • The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations Book Detail

  • Author : Ian Anderson
  • Release Date : 1992
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 122
  • ISBN 13 : 082182533X
  • File Size : 82,82 MB
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The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations by Ian Anderson PDF Summary

Book Description: This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centres on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coicides with a given system of ordinary differential equations. The authors rederive the basic necessary and sufficient conditions of Douglas for second order equations and extend them to equations of higher order using methods of the variational bicomplex of Tulcyjew, Vinogradov, and Tsujishita. The authors present an algorithm, based upon exterior differential systems techniques, for solving the inverse problem for second order equations. a number of new examples illustrate the effectiveness of this approach.

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