The Inverse Problem of the Calculus of Variations: Local and Global Theory (Atlantis Studies in Variational Geometry, 2) - Hardcover

 
9789462391086: The Inverse Problem of the Calculus of Variations: Local and Global Theory (Atlantis Studies in Variational Geometry, 2)
Hardcover
ISBN 10: 9462391084 ISBN 13: 9789462391086
Publisher: Atlantis Press, 2015

Synopsis

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).

"synopsis" may belong to another edition of this title.

From the Back Cover

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).

"About this title" may belong to another edition of this title.

Publisher
Atlantis Press
Publication date
2015
Language
English
ISBN 10 
9462391084
ISBN 13 
9789462391086
Binding
Hardcover
Number of pages
298
Editor
Zenkov Dmitry V.

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9789462391109: The Inverse Problem of the Calculus of Variations: Local and Global Theory

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ISBN 10:  9462391106 ISBN 13:  9789462391109
Publisher: Atlantis Press, 2015
Softcover