The Inverse Problem of the Calculus of Variations: Local and Global Theory (Atlantis Studies in Variational Geometry, 2)

ISBN 10: 9462391084 / ISBN 13: 9789462391086

Published by Atlantis Press, 2015

About this Item

Seller Inventory # I-9789462391086

Bibliographic Details

• Title: The Inverse Problem of the Calculus of Variations: Local and Global Theory (Atlantis Studies in Variational Geometry, 2)
• Publisher: Atlantis Press
• Publication Date: 2015
• Language: English
• ISBN 10: 9462391084
• ISBN 13: 9789462391086
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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).