The Inverse Problem of the Calculus of Variations
Local and Global Theory
Published on 27. October 2015
Book
Hardback
IX, 289 pages
978-94-6239-108-6 (ISBN)
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).
More details
Series
Edition
2015 ed.
Language
English
Place of publication
Paris
Netherlands
Target group
Professional and scholarly
Research
Illustrations
3 farbige Abbildungen
IX, 289 p. 3 illus. in color.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 22 mm
Weight
617 gr
ISBN-13
978-94-6239-108-6 (9789462391086)
DOI
10.2991/978-94-6239-109-3
Schweitzer Classification
Other editions
Additional editions
E-Book
10/2015
1st Edition
Atlantis Press
€53.49
Available for download
Content
The Helmholtz Conditions and the Method of Controlled Lagrangians.- The Sonin-Douglas Problem.- Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order Dynamics.- Variational Principles for Immersed Submanifolds.- Source Forms and their Variational Completions.- First-Order Variational Sequences in Field Theory.