The Inverse Problem of the Calculus of Variations
Local and Global Theory
(Sprache: Englisch)
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...
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Klappentext zu „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).
Inhaltsverzeichnis zu „The Inverse Problem of the Calculus of Variations “
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.
Bibliographische Angaben
- 2015, 1st ed. 2015, IX, 289 Seiten, 289 farbige Abbildungen, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Herausgegeben: Dmitry V. Zenkov
- Verlag: Springer, Berlin
- ISBN-10: 9462391084
- ISBN-13: 9789462391086
- Erscheinungsdatum: 27.10.2015
Sprache:
Englisch
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