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＜E-Book＞
Hamiltonian Structures and Generating Families / by Sergio Benenti
(Universitext. ISSN:21916675)

Edition	1st ed. 2011.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2011
Language	English
Size	XIV, 258 p. 50 illus : online resource
Authors	*Benenti, Sergio author SpringerLink (Online service)
Subjects	LCSH:Geometry, Differential LCSH:Mathematical physics LCSH:System theory LCSH:Control theory LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Differential Geometry FREE:Mathematical Physics FREE:Systems Theory, Control FREE:Global Analysis and Analysis on Manifolds
Notes	Preface.- Basic Notions of Calculus on Manifolds.- Relations.- Symplectic Relations on Symplectic Manifolds.- Symplectic Relations on Cotangent Bundles.- Canonical Lift on Cotangent Bundles.-The Geometry of the Hamilton-Jacobi Equation.- Hamiltonian Optics in Euclidean Spaces.- Control of Static Systems.- Supplementary Topics.- Global Hamilton Principal Functions on S2 and H2 -- References -- Index This book is an enhanced version of an earlier Russian edition. Besides thorough revisions, more emphasis was put on reordering the topics according to a category-theoretical view. This allows the mathematical results to be stated, proved, and understood in a much easier and elegant way. From the reviews of the Russian edition: "The main accent is shifted to the application . . . in geometrical optics, thermostatics and control theory, and not to the Hamiltonian mechanics only. . . . To make the book fairly self-contained, full details of basic definitions and all proofs are included. In this way, the majority of the text can be read without the prerequisite of a course in geometry. The excellent collection of examples illustrates the relatively hard and highly abstract mathematical theory and its hidden difficulties. . . . The book can rise real interest for specialists . . . .  The . . . book is a significant input in the modern symplectic geometry and its applications." (Andrey Tsiganov, St. Petersburg State University) Sergio Benenti is a professor of mathematical physics at Università di Torino, Italy. His current fields of research include symplectic geometry with applications to physical theories, Riemannian geometry with applications to the theory of the separation of variables in the Hamilton-Jacobi equation and in other relevant differential equations of physics, and mathematical models of the dynamics of non-holonomic systems HTTP:URL=https://doi.org/10.1007/978-1-4614-1499-5

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