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

Anderson, Ian; Thompson, Gerard

 
9780821825334: The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations
Brossura
ISBN 10: 082182533X ISBN 13: 9780821825334
Casa editrice: Amer Mathematical Society, 1992

Sinossi

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.

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Contenuti

The variational bicomplex for ordinary differential equations; First integrals and the inverse problem for second order ordinary differential equations; The inverse problem for fourth order ordinary differential equations; Exterior differential systems and the inverse problem for second order ordinary differential equations; Examples; The inverse problem for two dimensionalsprays.

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Editore
Amer Mathematical Society
Data di pubblicazione
1992
Lingua
Inglese
ISBN 10 
082182533X
ISBN 13 
9780821825334
Rilegatura
Copertina flessibile
Numero di pagine
110
Contatto del produttore
non disponibile
Persona responsabile
non disponibile