The Inverse Problem of the Calculus of Variations

Local and Global Theory
2015
ISBN: 978-94-6239-108-6
Verlag: Atlantis Press

Buch, Englisch, Band 2, 289 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 5738 g

Reihe: Atlantis Studies in Variational Geometry

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).

Zielgruppe

Research

Autoren/Hrsg.

Zenkov, Dmitry V.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung

Inhaltsverzeichnis

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.