9781402015748 - The Geometry of Higher-Order Hamilton Spaces: Applications to Hamiltonian Mechanics (Fundamental Theories of Physics, 132, Band 132) von Miron, R. (5 Ergebnisse)

Zustand: New. In.

Hardcover. Zustand: Brand New. 1st edition. 264 pages. 9.50x6.50x0.75 inches. In Stock.

Zustand: New. Presents an overview of higher-order Hamilton geometry with applications to higher-order Hamiltonian mechanics. This book contains the general theory of higher order Hamilton spaces, semisprays, the canonical nonlinear connection, the N-linear metrical connection, and the Riemannian almost contact metrical model of these spaces. Series: Fundamental Theories of Physics. Num Pages: 263 pages, biography. BIC Classification: PBMP; PDE; TBJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 235 x 155 x 15. Weight in Grams: 548. . 2003. Hardback. . . . . Books ship from the US and Ireland.

Gebunden. Zustand: New. 1 Geometry of the k-Tangent Bundle TkM.- 1.1 The Category of k-Accelerations Bundles.- 1.2 Liouville Vector Fields. k-Semisprays.- 1.3 Nonlinear Connections.- 1.4 The Dual Coefficients of a Nonlinear Connection.- 1.5 The Determination of a Nonlinear Connect.

Buch. Zustand: Neu. Neuware - Asisknown,theLagrangeandHamiltongeometrieshaveappearedrelatively recently [76, 86]. Since 1980thesegeometrieshave beenintensivelystudied bymathematiciansandphysicistsfromRomania,Canada,Germany,Japan, Russia, Hungary,e.S.A. etc. PrestigiousscientificmeetingsdevotedtoLagrangeandHamiltongeome tries and their applications have been organized in the above mentioned countries and a number ofbooks and monographs have been published by specialists in the field: R. Miron [94, 95], R. Mironand M. Anastasiei [99, 100], R. Miron, D. Hrimiuc, H. Shimadaand S.Sabau [115], P.L. Antonelli, R. Ingardenand M.Matsumoto [7]. Finslerspaces,whichformasubclassof theclassofLagrangespaces, havebeenthesubjectofsomeexcellentbooks, forexampleby:Yl.Matsumoto[76], M.AbateandG.Patrizio[1],D.Bao,S.S. Chernand Z.Shen [17]andA.BejancuandH.R.Farran [20]. Also, wewould liketopointoutthemonographsofM. Crampin [34], O.Krupkova [72] and D.Opri~,I.Butulescu [125],D.Saunders [144],whichcontainpertinentappli cationsinanalyticalmechanicsandinthetheoryofpartialdifferentialequa tions. Applicationsinmechanics, cosmology,theoreticalphysicsandbiology can be found in the well known books ofP.L. Antonelliand T.Zawstaniak [11], G.S. Asanov [14]' S. Ikeda [59], :VI. de LeoneandP.Rodrigues [73]. TheimportanceofLagrangeandHamiltongeometriesconsistsofthefact that variational problems for important Lagrangiansor Hamiltonians have numerous applicationsinvariousfields, such asmathematics, thetheoryof dynamicalsystems, optimalcontrol, biology,andeconomy. Inthisrespect, P.L. Antonelli'sremark isinteresting: 'ThereisnowstrongevidencethatthesymplecticgeometryofHamilto niandynamicalsystemsisdeeplyconnectedtoCartangeometry,thedualof Finslergeometry', (seeV.I.Arnold,I.M.GelfandandV.S.Retach [13]). The above mentioned applications have also imposed the introduction x RaduMiron ofthe notionsofhigherorder Lagrangespacesand, ofcourse, higherorder Hamilton spaces. The base manifolds ofthese spaces are bundles ofaccel erations ofsuperior order. The methods used in the construction ofthese geometries are the natural extensions ofthe classical methods used in the edification ofLagrange and Hamilton geometries. These methods allow us to solvean old problemofdifferentialgeometryformulated by Bianchiand Bompiani [94]morethan 100yearsago,namelytheproblemofprolongation ofaRiemannianstructure gdefinedonthebasemanifoldM,tothetangent k bundleT M, k 1. Bymeansofthissolutionofthe previousproblem, we canconstruct, for thefirst time,goodexamplesofregularLagrangiansand Hamiltoniansofhigherorder.