The Inverse Problem of the Calculus of Variations
Local and Global Theory| By: | Dmitry V. Zenkov |
| Publisher: | Springer Nature |
| Print ISBN: | 9789462391086 |
| eText ISBN: | 9789462391093 |
| Edition: | 0 |
| Copyright: | 2015 |
| Format: | Page Fidelity |
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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).