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OverviewThe 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). Full Product DetailsAuthor: Dmitry V. ZenkovPublisher: Atlantis Press (Zeger Karssen) Imprint: Atlantis Press (Zeger Karssen) Edition: 1st ed. 2015 Volume: 2 Dimensions: Width: 15.50cm , Height: 1.80cm , Length: 23.50cm Weight: 5.738kg ISBN: 9789462391086ISBN 10: 9462391084 Pages: 289 Publication Date: 27 October 2015 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsThe 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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