The Inverse Problem of the Calculus of Variations
Local and Global Theory
Seiten
2015
|
2015 ed.
Atlantis Press (Zeger Karssen) (Verlag)
9789462391086 (ISBN)
Atlantis Press (Zeger Karssen) (Verlag)
9789462391086 (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-13 | 9789462391086 / 9789462391086 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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