The Inverse Problem of the Calculus of Variations [electronic resource] : Local and Global Theory / edited by Dmitry V. Zenkov
- Paris : Atlantis Press : Imprint: Atlantis Press, 2015.
- 1st ed. 2015.
- Physical Description:
- IX, 289 p. 3 illus. in color. online resource
- Additional Creators:
- Zenkov, Dmitry V. and SpringerLink (Online service)
- Atlantis Studies in Variational Geometry, 2214-0700 ; 2
- 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.
- 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).
- Digital File Characteristics:
- text file PDF
- AVAILABLE ONLINE TO AUTHORIZED PSU USERS.
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