The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

American Mathematical Society

Softcover

ISBN 10: 082182533X ISBN 13: 9780821825334

Publisher: American Mathematical Society, 1993

Synopsis

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. the various possible solutions to the inverse problem for these equations are distinguished by geometric properties of the Ricci tensor.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1993
• Language: English
• ISBN 10: 082182533X
• ISBN 13: 9780821825334
• Binding: Paperback
• Number of pages: 110