Click Here to Download: https://ouo.io/l3kpzB The Inverse Problem of the Calculus of Variations Local and Global Theory By: Dmitry V. Zenkov Publisher: Atlantis Press Print ISBN: 9789462391086, 9462391084 eText ISBN: 9789462391093, 9462391092 Copyright year: 2015 Format: PDF Available from $ 99.00 USD SKU 9789462391093 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).
