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＜電子ブック＞
The Inverse Problem of the Calculus of Variations : Local and Global Theory / edited by Dmitry V. Zenkov
(Atlantis Studies in Variational Geometry. ISSN:22140719 ; 2)

版	1st ed. 2015.
出版者	(Paris : Atlantis Press : Imprint: Atlantis Press)
出版年	2015
本文言語	英語
大きさ	IX, 289 p. 3 illus. in color : online resource
著者標目	Zenkov, Dmitry V editor SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Geometry, Differential LCSH:Gravitation FREE:Calculus of Variations and Optimization FREE:Global Analysis and Analysis on Manifolds FREE:Differential Geometry FREE:Classical and Quantum Gravity
一般注記	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) HTTP:URL=https://doi.org/10.2991/978-94-6239-109-3

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