Hamiltonian structures and generating families
著者
書誌事項
Hamiltonian structures and generating families
（Universitext）
Springer, c2011
- : pbk
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注記
Translated from the Russian
Includes bibliographical references (p. 247-251) and index
内容説明・目次
内容説明
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)
目次
Preface.- 1 Basic Notions of Calculus on Manifolds.- 2 Relations.- 3 Symplectic Relations on Symplectic Manifolds.- 4 Symplectic Relations on Cotangent Bundles.- 5 Canonical Lift on Cotangent Bundles.- 6 The Geometry of the Hamilton-Jacobi Equation.- 7 Hamiltonian Optics in Euclidean Spaces.- 8 Control of Static Systems.- 9 Supplementary Topics.- 10 Global Hamilton Principal Functions on S2 and H2.- References.- Index.
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