The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations. (Memoirs of the American Mathematical Society 473).

Anderson, Ian and Gerard Thompson:

ISBN 10: 082182533X / ISBN 13: 9780821825334

Published by Providence, American Mathematical Society, 1992

About this Item

110 Seiten. Ehem. Bibliotheksexemplar mit Signaturen und Stempeln. Einband leicht berieben und an den Ecken leicht angeknickt. Ansonsten gut erhalten. 082182533X Sprache: Englisch Gewicht in Gramm: 1200.

Seller Inventory # 100571

Bibliographic Details

• Title: The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations. (Memoirs of the American Mathematical Society 473).
• Publisher: Providence, American Mathematical Society
• Publication Date: 1992
• Language: English
• ISBN 10: 082182533X
• ISBN 13: 9780821825334
• Binding: Softcover/Paperback
• Condition: Gut
• Weight: 1200 grams
• Seller catalogs:
  • Mathematik, Physik, Astronomie

About this title

Synopsis

This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centers on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coincides 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 Lagrangian 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 monograph 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.