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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 /
Catalogue Information
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).
Internet Site http://dx.doi.org/10.2991/978-94-6239-109-3
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