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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
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Atlantis Studies in Variational Geometry
- Call Number
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-
- Publisher
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Atlantis Press Paris :
Atlantis Press Paris.,
2015
- Collation
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IX, 289, 3 illustrations in colour
- Language
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English
- ISBN/ISSN
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978-94-6239-109-3
- Classification
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NONE
- Content Type
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text
- Media Type
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computer
- Carrier Type
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-
- Edition
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1
- Subject(s)
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- Specific Detail Info
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- Statement of Responsibility
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Dmitry V. Zenkov
Other Information
- Cataloger
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Suwardi
- Source
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https://link.springer.com/book/10.2991/978-94-6239-109-3
- Validator
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-
Other version/related
No other version available
File Attachment
- 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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