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The Inverse Problem of the Calculus of Variations

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).

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Detail Information
Series Title
Atlantis Studies in Variational Geometry
Call Number
-
Publisher
Atlantis Press Paris : Atlantis Press Paris.,
Collation
IX, 289, 3 illustrations in colour
Language
English
ISBN/ISSN
978-94-6239-109-3
Classification
NONE
Content Type
text
Media Type
computer
Carrier Type
-
Edition
1
Subject(s)
Calculus of Variations
Optimization,
Classical
Specific Detail Info
-
Statement of Responsibility
Other Information
Cataloger
Suwardi
Source
https://link.springer.com/book/10.2991/978-94-6239-109-3
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  • The Inverse Problem of the Calculus of Variations
    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).
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