The Inverse Problem of the Calculus of Variations

Local and Global Theory
Herausgegeben:Zenkov, Dmitry V.

• Gebundenes Buch

Produktbeschreibung

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).

Produktdetails

• Atlantis Studies in Variational Geometry 2
• Verlag: Atlantis Press / Springer, Berlin
• Artikelnr. des Verlages: 978-94-6239-108-6
• 1st ed. 2015
• Seitenzahl: 300
• Erscheinungstermin: 27. Oktober 2015
• Englisch
• Abmessung: 241mm x 160mm x 22mm
• Gewicht: 590g
• ISBN-13: 9789462391086
• ISBN-10: 9462391084
• Artikelnr.: 41871947

Inhaltsangabe

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.