The Inverse Problem of the Calculus of Variations
Local and Global Theory
Seiten
2015
|
2015 ed.
Atlantis Press (Zeger Karssen) (Verlag)
978-94-6239-108-6 (ISBN)
Atlantis Press (Zeger Karssen) (Verlag)
978-94-6239-108-6 (ISBN)
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).
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).
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.
| Reihe/Serie | Atlantis Studies in Variational Geometry ; 2 |
|---|---|
| Zusatzinfo | 3 Illustrations, color; IX, 289 p. 3 illus. in color. |
| Verlagsort | Paris |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Naturwissenschaften ► Geowissenschaften ► Geophysik | |
| Naturwissenschaften ► Physik / Astronomie | |
| Schlagworte | Euler-Lagrange form • Helmholtz conditions • Lagrangian • Source form • Variational sequence |
| ISBN-10 | 94-6239-108-4 / 9462391084 |
| ISBN-13 | 978-94-6239-108-6 / 9789462391086 |
| Zustand | Neuware |
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