The Inverse Problem of the Calculus of Variations Gebunden

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) - Inve rse 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).