The Geometry of Higher-Order Hamilton Spaces: Applications to Hamiltonian Mechanics - Couverture rigide

Miron, R

Couverture rigide

ISBN 10 : 1402015747 ISBN 13 : 9781402015748

Editeur : Springer, 2003

Synopsis

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2003
• Langue: anglais
• ISBN 10: 1402015747
• ISBN 13: 9781402015748
• Reliure: Relié
• Nombre de pages: 247
• Coordonnées du fabricant: non disponible
• Personne responsable: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Allemagne