The Inverse Problem of the Calculus of Variations: Local and Global Theory by Dmitry V. ZenkovThe Inverse Problem of the Calculus of Variations: Local and Global Theory by Dmitry V. Zenkov

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

byDmitry V. Zenkov

Hardcover | October 27, 2015

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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).
Title:The Inverse Problem of the Calculus of Variations: Local and Global TheoryFormat:HardcoverDimensions:289 pages, 23.5 × 15.5 × 0.03 inPublished:October 27, 2015Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9462391084

ISBN - 13:9789462391086

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Table of Contents

The Helmholtz Conditions and the Method of Controlled Lagrangians.- The Sonin-Douglas Problem.- Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order Dynamics.- Variational Principles for Immersed Submanifolds.- Source Forms and their Variational Completions.- First-Order Variational Sequences in Field Theory.