The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations, Issue 473 (Google eBook)

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American Mathematical Soc., 1992 - Mathematics - 110 pages
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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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Contents

1 INTRODUCTION
1
EQUATIONS
12
3 FIRST INTEGRALS AND THE INVERSE PROBLEM FOR SECOND ORDER EQUATIONS
27
4 THE INVERSE PROBLEM FOR FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS
35
5 EXTERIOR DIFFERENTIAL SYSTEMS AND THE INVERSE PROBLEM FOR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS
50
6 EXAMPLES
64
7 THE INVERSE PROBLEM FOR TWO DIMENSIONAL SPRAYS
88
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Philosophy of Physics: Part B.

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