The inverse problem of the calculus of variations for ordinary differential equations
Author(s)
Bibliographic Information
The inverse problem of the calculus of variations for ordinary differential equations
（Memoirs of the American Mathematical Society, no. 473）
American Mathematical Society, 1992
Available at 22 libraries
Note
"July 1992, volume 98, number 473 (end of volume)"
Includes bibliographical references (p. 108-110)
Description and Table of Contents
Description
This monograph explores various aspects of the inverse problem of the calculus of ariations 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. What emerges is a fundamental dichotomy between second and higher order systems: the most general Lagranigian for any higher order system can depend only upon finitely many constants. 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. The monogrpah also contains a study of the inverse problem for a pair of geodesic equations arising from a two dimensional symmetric affine connection.
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