The Geometry of Higher-Order Lagrange Spaces, R. Miron

Автор: R. Miron
Название: The Geometry of Higher-Order Lagrange Spaces
ISBN: 079234393X ISBN-13(EAN): 9780792343936
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Описание: Devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations, this volume presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. It is suitable for scientists whose work involves differential geometry and mechanics of particles and systems.

Автор: R. Miron; Dragos Hrimiuc; Hideo Shimada; Sorin V.
Название: The Geometry of Hamilton and Lagrange Spaces
ISBN: 0792369262 ISBN-13(EAN): 9780792369264
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Описание: It reveals new concepts and geometrical objects of Hamilton spaces that are dual to those which are similar in Lagrange spaces. Following this duality Cartan spaces introduced and studied in [98], [99],..., are, roughly speaking, the Legendre duals of certain Finsler spaces [98], [66], [67].

Автор: P.L. Antonelli; R. Miron
Название: Lagrange and Finsler Geometry
ISBN: 0792338731 ISBN-13(EAN): 9780792338734
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Описание: The differential geometry of a regular Lagrangian is more involved than that of classical kinetic energy and consequently is far from being Riemannian. This collection of papers covers higher order Lagrange geometry, the theory of -Lagrange manifolds, electromagnetic theory and neurophysiology.

Автор: Lagrange, J.L
Название: Analytical Mechanics
ISBN: 9048147794 ISBN-13(EAN): 9789048147793
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Описание: to the English translation of Lagrange's Mecanique Analytique Lagrange's Mecanique Analytique appeared early in 1788 almost exactly one cen- tury after the publication of Newton's Principia Mathematica. It marked the culmination of a line of research devoted to recasting Newton's synthetic, geomet- ric methods in the analytic style of the Leibnizian calculus. Its sources extended well beyond the physics of central forces set forth in the Principia. Continental au- thors such as Jakob Bernoulli, Daniel Bernoulli, Leonhard Euler, Alexis Clairaut and Jean d'Alembert had developed new concepts and methods to investigate problems in constrained interaction, fluid flow, elasticity, strength of materials and the operation of machines. The Mecanique Analytique was a remarkable work of compilation that became a fundamental reference for subsequent research in exact science. During the eighteenth century there was a considerable emphasis on extending the domain of analysis and algorithmic calculation, on reducing the dependence of advanced mathematics on geometrical intuition and diagrammatic aids. The analytical style that characterizes the Mecanique Analytique was evident in La- grange's original derivation in 1755 of the 8-algorithm in the calculus of variations. It was expressed in his consistent attempts during the 1770s to prove theorems of mathematics and mechanics that had previously been obtained synthetically. The scope and distinctiveness of his 1788 treatise are evident if one compares it with an earlier work of similar outlook, Euler's Mechanica sive Motus Scientia Analyt- 1 ice Exposita of 1736.

Автор: Harold E. Trease; Martin F. Fritts; W. Patrick Cro
Название: Advances in the Free-Lagrange Method
ISBN: 3662138077 ISBN-13(EAN): 9783662138076
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Описание: Proceedings of the Next Free-Lagrange Conference Held at Jackson Lake Lodge, Moran, WY, USA, 3-7 June 1990

Автор: A. Boissonnade; J.L. Lagrange; V.N. Vagliente
Название: Analytical Mechanics
ISBN: 0792343492 ISBN-13(EAN): 9780792343493
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Описание: Offering an account of Lagrangian mechanics, this work uses the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve the problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d`Alembert`s Principle - in order to develop the Lagrangian equations of motion.

Автор: Alexander M. Rubinov; Xiao-qi Yang
Название: Lagrange-type Functions in Constrained Non-Convex Optimization
ISBN: 1461348218 ISBN-13(EAN): 9781461348214
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Описание: Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimiza- tion problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints.

Автор: R. Miron
Название: The Geometry of Higher-Order Hamilton Spaces
ISBN: 940103995X ISBN-13(EAN): 9789401039956
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Описание: 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.