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).
| Serija: | Atlantis Studies in Variational Geometry |
| Leidėjas: | Atlantis Press |
| Išleidimo metai: | 2015 |
| Knygos puslapių skaičius: | 300 |
| ISBN-10: | 9462391084 |
| ISBN-13: | 9789462391086 |
| Formatas: | 241 x 160 x 22 mm. Knyga kietu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „The Inverse Problem of the Calculus of Variations: Local and Global Theory“
