The Inverse Problem of the Calculus of Variations

Name: The Inverse Problem of the Calculus of Variations
Price: 101.37 AUD
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ISBN: 9789462391086

Local and Global Theory

Dmitry V. Zenkov

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Hardback

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English

Atlantis Press (Zeger Karssen)
27 October 2015

Calculus of variations; Numerical analysis; Differential & Riemannian geometry; Gravity

Series: 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).

Edited by: Dmitry V. Zenkov
Imprint: Atlantis Press (Zeger Karssen)
Edition: 2015 ed.
Volume: 2
Dimensions: Height: 235mm, Width: 155mm, Spine: 18mm
Weight: 5.738kg
ISBN: 9789462391086
ISBN 10: 9462391084
Series: Atlantis Studies in Variational Geometry
Pages: 289
Publication Date: 27 October 2015
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.