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Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
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The Inverse Problem of the Calculus of Variations - Local and Global Theory (Hardcover, 1st ed. 2015)
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The Inverse Problem of the Calculus of Variations - Local and Global Theory (Hardcover, 1st ed. 2015)
Series: Atlantis Studies in Variational Geometry, 2
Expected to ship within 12 - 17 working days
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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).
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