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

The Inverse Problem of the Calculus of Variations: Local and Global Theory /
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Field name Details
Dewey Class 515.64
Title The Inverse Problem of the Calculus of Variations ([EBook]) : Local and Global Theory / / edited by Dmitry V. Zenkov.
Added Personal Name Zenkov, Dmitry V. editor.
Other name(s) SpringerLink (Online service)
Edition statement 1st ed. 2015.
Publication Paris : : Atlantis Press : : Imprint: Atlantis Press, , 2015.
Physical Details IX, 289 p. 3 illus. in color. : online resource.
Series Atlantis Studies in Variational Geometry 2214-0700 ; ; 2
ISBN 9789462391093
Summary Note 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).:
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
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