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The inverse problem of the calculus ...

Zenkov, Dmitry V.

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The inverse problem of the calculus of variations = local and global theory /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The inverse problem of the calculus of variations/ edited by Dmitry V. Zenkov.
Reminder of title:	local and global theory /
other author:	Zenkov, Dmitry V.
Published:	Paris :Atlantis Press : : 2015.,
Description:	ix, 289 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Calculus of variations. -
Online resource:	http://dx.doi.org/10.2991/978-94-6239-109-3
ISBN:	9789462391093

The inverse problem of the calculus of variations = local and global theory /
The inverse problem of the calculus of variationslocal and global theory /[electronic resource] :edited by Dmitry V. Zenkov. - Paris :Atlantis Press :2015. - ix, 289 p. :ill., digital ;24 cm. - Atlantis studies in variational geometry,v.22214-0700 ;. - Atlantis studies in variational geometry ;v.1..

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.

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)

ISBN: 9789462391093

Standard No.: 10.2991/978-94-6239-109-3doiSubjects--Topical Terms:

516604
Calculus of variations.

LC Class. No.: QA315

Dewey Class. No.: 515.64

The inverse problem of the calculus of variations = local and global theory /
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245 0 4 $a The inverse problem of the calculus of variations $h [electronic resource] : $b local and global theory / $c edited by Dmitry V. Zenkov.
260 $a Paris : $b Atlantis Press : $b Imprint: Atlantis Press, $c 2015.
300 $a ix, 289 p. : $b ill., digital ; $c 24 cm.
490 1 $a Atlantis studies in variational geometry, $x 2214-0700 ; $v v.2
505 0 $a 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.
520 $a 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)
650 0 $a Calculus of variations. $3 516604
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650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
650 2 4 $a Differential Geometry. $3 891003
650 2 4 $a Classical and Quantum Gravitation, Relativity Theory. $3 1067066
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