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The Inverse Problem of the Calculus of Variations : Local and Global Theory / edited by Dmitry V. Zenkov.
Springer Nature - Springer Mathematics and Statistics eBooks 2015 English International Available online
View online- Format:
- Book
- Series:
- Atlantis Studies in Variational Geometry, 2214-0719 ; 2
- Language:
- English
- Subjects (All):
- Mathematical optimization.
- Calculus of variations.
- Global analysis (Mathematics).
- Manifolds (Mathematics).
- Geometry, Differential.
- Gravitation.
- Calculus of Variations and Optimization.
- Global Analysis and Analysis on Manifolds.
- Differential Geometry.
- Classical and Quantum Gravity.
- Local Subjects:
- Calculus of Variations and Optimization.
- Global Analysis and Analysis on Manifolds.
- Differential Geometry.
- Classical and Quantum Gravity.
- Physical Description:
- 1 online resource (296 p.)
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Paris : Atlantis Press : Imprint: Atlantis Press, 2015.
- Language Note:
- English
- Summary:
- 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:
- 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.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references and index.
- ISBN:
- 94-6239-109-2
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