{"product_id":"9789462391086","title":"The Inverse Problem of the Calculus of Variations: Local and Global Theory","description":"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).","brand":"Atlantis Press","offers":[{"title":"Default Title","offer_id":47059720700144,"sku":"9789462391086","price":109.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789462391086_p0.jpg?v=1763676559","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789462391086","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}