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The Inverse Problem of the Calculus of Variations: Local and Global Theory /
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Catalogue Record 31077
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Catalogue Information
Field name
Details
Dewey Class
515.64
Title
The Inverse Problem of the Calculus of Variations ([EBook]) : Local and Global Theory / / edited by Dmitry V. Zenkov.
Added Personal Name
Zenkov, Dmitry V.
editor.
Other name(s)
SpringerLink (Online service)
Edition statement
1st ed. 2015.
Publication
Paris : : Atlantis Press : : Imprint: Atlantis Press, , 2015.
Physical Details
IX, 289 p. 3 illus. in color. : online resource.
Series
Atlantis Studies in Variational Geometry
2214-0700 ; ; 2
ISBN
9789462391093
Summary Note
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).:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
http://dx.doi.org/10.2991/978-94-6239-109-3
Links to Related Works
Subject References:
Calculus of variations
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Calculus of variations and optimal control; optimization
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Classical and Quantum Gravitation, Relativity Theory
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Differential Geometry
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Global Analysis and Analysis on Manifolds
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Global analysis (Mathematics)
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Gravitation
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Manifolds (Mathematics)
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Mathematics
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Authors:
Zenkov, Dmitry V.
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Corporate Authors:
SpringerLink (Online service)
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Series:
Atlantis Studies in Variational Geometry
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Classification:
515.64
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