The Inverse Problem of the Calculus of Variations
Title | The Inverse Problem of the Calculus of Variations PDF eBook |
Author | Dmitry V. Zenkov |
Publisher | Springer |
Pages | 296 |
Release | 2015-10-15 |
Genre | Mathematics |
ISBN | 9462391092 |
The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).
The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations
Title | The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations PDF eBook |
Author | Ian Anderson |
Publisher | American Mathematical Soc. |
Pages | 122 |
Release | 1992 |
Genre | Mathematics |
ISBN | 082182533X |
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.
Studies of the Inverse Problem of the Calculus of Variations
Title | Studies of the Inverse Problem of the Calculus of Variations PDF eBook |
Author | Nathan Abraham Moscovitch |
Publisher | |
Pages | 39 |
Release | 1937 |
Genre | Calculus of variations |
ISBN |
An Inverse Problem of the Calculus of Variations
Title | An Inverse Problem of the Calculus of Variations PDF eBook |
Author | Lincoln La Paz |
Publisher | |
Pages | 72 |
Release | 1928 |
Genre | Calculus of variations |
ISBN |
Inverse Problem of the Calculus of Variations
Title | Inverse Problem of the Calculus of Variations PDF eBook |
Author | D. R. Davis |
Publisher | |
Pages | |
Release | |
Genre | |
ISBN |
Certain Inverse Problems in the Calculus of Variations
Title | Certain Inverse Problems in the Calculus of Variations PDF eBook |
Author | Amor Henry Schlenker |
Publisher | |
Pages | 96 |
Release | 1932 |
Genre | |
ISBN |
Aspects of the Inverse Problem in the Calculus of Variations
Title | Aspects of the Inverse Problem in the Calculus of Variations PDF eBook |
Author | Jonathan E. Aldridge |
Publisher | |
Pages | 181 |
Release | 2003 |
Genre | Calculus of variations |
ISBN |