000 03536nam a22005055i 4500
001 978-1-4614-1499-5
003 DE-He213
005 20140220083733.0
007 cr nn 008mamaa
008 110907s2011 xxu| s |||| 0|eng d
020 _a9781461414995
_9978-1-4614-1499-5
024 7 _a10.1007/978-1-4614-1499-5
_2doi
050 4 _aQA614-614.97
072 7 _aPBKS
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a514.74
_223
100 1 _aBenenti, Sergio.
_eauthor.
245 1 0 _aHamiltonian Structures and Generating Families
_h[electronic resource] /
_cby Sergio Benenti.
264 1 _aNew York, NY :
_bSpringer New York,
_c2011.
300 _aXIV, 258p. 50 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _aPreface.- 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.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aGlobal analysis.
650 0 _aSystems theory.
650 0 _aGlobal differential geometry.
650 1 4 _aMathematics.
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
650 2 4 _aSystems Theory, Control.
650 2 4 _aMathematical Applications in the Physical Sciences.
650 2 4 _aDifferential Geometry.
650 2 4 _aMathematical Physics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461414988
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-1499-5
912 _aZDB-2-SMA
999 _c106292
_d106292