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Atlantis Studies in Variational Geometry

The Inverse Problem of the Calculus of Variations

Local and Global Theory

Editors: Zenkov, Dmitry V. (Ed.)

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  • Unified exposition of the inverse variational problem for ordinary and partial differential equations and for equations on manifolds
  • First systematic contribution to the global inverse problem of the calculus of variations based on modern differential geometry and algebraic topology
  • Selected applications of the inverse problem in geometry, optimal control theory and modern theoretical physics (higher-order mechanics and general relativity)
  • Prepares the reader for research in the local and global inverse problem using variational sequence theory and its consequences based on elementary sheaf theory
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eBook $84.99
price for USA in USD (gross)
  • ISBN 978-94-6239-109-3
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  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-94-6239-108-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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).

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-94-6239-109-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-94-6239-108-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Inverse Problem of the Calculus of Variations
Book Subtitle
Local and Global Theory
Editors
  • Dmitry V. Zenkov
Series Title
Atlantis Studies in Variational Geometry
Series Volume
2
Copyright
2015
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the author(s)
eBook ISBN
978-94-6239-109-3
DOI
10.2991/978-94-6239-109-3
Hardcover ISBN
978-94-6239-108-6
Series ISSN
2214-0700
Edition Number
1
Number of Pages
IX, 289
Number of Illustrations
3 illustrations in colour
Topics