| EAN: | 9789462391086 |
|---|---|
| Sachgruppe: | Mathematik |
| Sprache: | Englisch |
| Seitenzahl: | 300 |
| Produktart: | Gebunden |
| Herausgeber: | Zenkov, Dmitry V. |
| Veröffentlichungsdatum: | 27.10.2015 |
| Untertitel: | Local and Global Theory |
| Schlagworte: | Differenzialgeometrie Differenzialgeometrie / Riemann Geometrie / Differenzialgeometrie Gravitation Mathematik Optimierung Physik Relativitätstheorie Riemannsche Geometrie Schwerkraft Variationsrechnung |
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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).
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