TY  - BOOK
AU  - Zenkov,Dmitry V.
ED  - SpringerLink (Online service)
TI  - The Inverse Problem of the Calculus of Variations: Local and Global Theory 
T2  - Atlantis Studies in Variational Geometry,
SN  - 9789462391093
AV  - QA315-316 
U1  - 515.64 23
PY  - 2015///
CY  - Paris
PB  - Atlantis Press, Imprint: Atlantis Press
KW  - Mathematics
KW  - Global analysis (Mathematics)
KW  - Manifolds (Mathematics)
KW  - Differential geometry
KW  - Calculus of variations
KW  - Gravitation
KW  - Calculus of Variations and Optimal Control; Optimization
KW  - Global Analysis and Analysis on Manifolds
KW  - Differential Geometry
KW  - Classical and Quantum Gravitation, Relativity Theory
N1  - 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
N2  - 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)
UR  - http://dx.doi.org/10.2991/978-94-6239-109-3
ER  -