Atlantis Studies in Variational Geometry - Böcker
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4 produkter
4 produkter
Del 1 - Atlantis Studies in Variational Geometry
Introduction to Global Variational Geometry
Inbunden, Engelska, 2015
955 kr
Skickas inom 10-15 vardagar
Introduction to Global Variational Geometry
Del 2 - Atlantis Studies in Variational Geometry
Inverse Problem of the Calculus of Variations
Local and Global Theory
Inbunden, Engelska, 2015
534 kr
Skickas inom 10-15 vardagar
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).
Del 3 - Atlantis Studies in Variational Geometry
Noether's Theorems
Applications in Mechanics and Field Theory
Inbunden, Engelska, 2016
1 008 kr
Skickas inom 10-15 vardagar
The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.
Del 4 - Atlantis Studies in Variational Geometry
Cartan Geometries and their Symmetries
A Lie Algebroid Approach
Inbunden, Engelska, 2016
1 008 kr
Skickas inom 10-15 vardagar
In this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle, and the connections on such groupoids together with their symmetries. We also see how the infinitesimal approach, using Lie algebroids rather than Lie groupoids, and in particular using Lie algebroids of vector fields along the projection of the fibre bundle, may be of benefit.We then introduce Cartan geometries, together with a number of tools we shall use to study them. We take, as particular examples, the four classical types of geometry: affine, projective, Riemannian and conformal geometry. We also see how our approach can start to fit into a more general theory. Finally, we specialize to the geometries (affine and projective) associated with path spaces and geodesics, and consider their symmetries and other properties.