The Inverse Problem of the Calculus of Variations [electronic resource] : Local and Global Theory / edited by Dmitry V. Zenkov.
Material type:
TextSeries: Atlantis Studies in Variational Geometry ; 2Publisher: Paris : Atlantis Press : Imprint: Atlantis Press, 2015Edition: 1st ed. 2015Description: IX, 289 p. 3 illus. in color. online resourceContent type: - text
- computer
- online resource
- 9789462391093
- Mathematics
- Global analysis (Mathematics)
- Manifolds (Mathematics)
- Differential geometry
- Calculus of variations
- Gravitation
- Mathematics
- Calculus of Variations and Optimal Control; Optimization
- Global Analysis and Analysis on Manifolds
- Differential Geometry
- Classical and Quantum Gravitation, Relativity Theory
- 515.64 23
- QA315-316
- QA402.3
- QA402.5-QA402.6
| Item type | Current library | Collection | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|---|
eBook
|
e-Library | EBook | Available |
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).