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The Geometry Of Hamilton And Lagrange Spaces

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The Geometry Of Hamilton And Lagrange Spaces

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Author : R. Miron
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-05-31

The Geometry Of Hamilton And Lagrange Spaces written by R. Miron and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-31 with Mathematics categories.

This monograph presents for the first time the foundations of Hamilton Geometry. The concept of Hamilton Space, introduced by the first author and investigated by the authors, opens a new domain in differential geometry with large applications in mechanics, physics, optimal control, etc. The book consists of thirteen chapters. The first three chapters present the topics of the tangent bundle geometry, Finsler and Lagrange spaces. Chapters 4-7 are devoted to the construction of geometry of Hamilton spaces and the duality between these spaces and Lagrange spaces. The dual of a Finsler space is a Cartan space. Even this notion is completely new, its geometry has the same symmetry and beauty as that of Finsler spaces. Chapter 8 deals with symplectic transformations of cotangent bundle. The last five chapters present, for the first time, the geometrical theory and applications of Higher-Order Hamilton spaces. In particular, the case of order two is presented in detail. Audience: mathematicians, geometers, physicists, and mechanicians. This volume can also be recommended as a supplementary graduate text.

The Geometry Of Hamilton And Lagrange Spaces

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Author : R. Miron
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11

The title of this book is no surprise for people working in the field of Analytical Mechanics. However, the geometric concepts of Lagrange space and Hamilton space are completely new. The geometry of Lagrange spaces, introduced and studied in [76],[96], was ext- sively examined in the last two decades by geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and U.S.A. Many international conferences were devoted to debate this subject, proceedings and monographs were published [10], [18], [112], [113],... A large area of applicability of this geometry is suggested by the connections to Biology, Mechanics, and Physics and also by its general setting as a generalization of Finsler and Riemannian geometries. The concept of Hamilton space, introduced in [105], [101] was intensively studied in [63], [66], [97],... and it has been successful, as a geometric theory of the Ham- tonian function the fundamental entity in Mechanics and Physics. The classical Legendre’s duality makes possible a natural connection between Lagrange and - miltonspaces. 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]. The above arguments make this monograph a continuation of [106], [113], emphasizing the Hamilton geometry.

The Geometry Of Higher Order Hamilton Spaces

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Author : R. Miron
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-31

The Geometry Of Higher Order Hamilton Spaces written by R. Miron and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-31 with Mathematics categories.

This book is the first to present an overview of higher-orderHamilton geometry with applications to higher-order Hamiltonianmechanics. It is a direct continuation of the book "The Geometry ofHamilton and" "Lagrange Spaces," (Kluwer Academic Publishers,2001). It contains the general theory of higher order Hamilton spaces"H," "k>=1," semisprays, the canonical nonlinearconnection, the N-linear metrical connection and their structureequations, and the Riemannian almost contact metrical model of thesespaces. In addition, the volume also describes new developments suchas variational principles for higher order Hamiltonians; Hamilton-Jacobi equations; higher order energies and law ofconservation; Noether symmetries; Hamilton subspaces of order k andtheir fundamental equations. The duality, via Legendre transformation, between Hamilton spaces of order k and Lagrange spaces of the sameorder is pointed out. Also, the geometry of Cartan spaces of order k=1 is investigated in detail. This theory is useful intheconstruction of geometrical models in theoretical physics, mechanics, dynamical systems, optimal control, biology, economy etc."Audience: " Mathematicians, geometers, physicists and engineers.The volume can be recommended as a supplementary graduate text.

The Geometry Of Hamilton And Lagrange Spaces

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Author : R. Miron
language : en
Publisher:
Release Date : 2014-03-14

The Geometry Of Hamilton And Lagrange Spaces written by R. Miron and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-14 with categories.

The Geometry Of Higher Order Hamilton Spaces

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Author : R. Miron
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

This book is the first to present an overview of higher-order Hamilton geometry with applications to higher-order Hamiltonian mechanics. It is a direct continuation of the book The Geometry of Hamilton and Lagrange Spaces, (Kluwer Academic Publishers, 2001). It contains the general theory of higher order Hamilton spaces H(k)n, k>=1, semisprays, the canonical nonlinear connection, the N-linear metrical connection and their structure equations, and the Riemannian almost contact metrical model of these spaces. In addition, the volume also describes new developments such as variational principles for higher order Hamiltonians; Hamilton-Jacobi equations; higher order energies and law of conservation; Noether symmetries; Hamilton subspaces of order k and their fundamental equations. The duality, via Legendre transformation, between Hamilton spaces of order k and Lagrange spaces of the same order is pointed out. Also, the geometry of Cartan spaces of order k =1 is investigated in detail. This theory is useful in the construction of geometrical models in theoretical physics, mechanics, dynamical systems, optimal control, biology, economy etc.

The Geometry Of Higher Order Lagrange Spaces

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Author : R. Miron
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

The Geometry Of Higher Order Lagrange Spaces written by R. Miron and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations. It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved. Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with. Applications to higher-order analytical mechanics and theoretical physics are included as well. Audience: This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology.

Complex Spaces In Finsler Lagrange And Hamilton Geometries

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Author : Gheorghe Munteanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-03

Complex Spaces In Finsler Lagrange And Hamilton Geometries written by Gheorghe Munteanu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-03 with Mathematics categories.

From a historical point of view, the theory we submit to the present study has its origins in the famous dissertation of P. Finsler from 1918 ([Fi]). In a the classical notion also conventional classification, Finsler geometry has besides a number of generalizations, which use the same work technique and which can be considered self-geometries: Lagrange and Hamilton spaces. Finsler geometry had a period of incubation long enough, so that few math ematicians (E. Cartan, L. Berwald, S.S. Chem, H. Rund) had the patience to penetrate into a universe of tensors, which made them compare it to a jungle. To aU of us, who study nowadays Finsler geometry, it is obvious that the qualitative leap was made in the 1970's by the crystallization of the nonlinear connection notion (a notion which is almost as old as Finsler space, [SZ4]) and by work-skills into its adapted frame fields. The results obtained by M. Matsumoto (coUected later, in 1986, in a monograph, [Ma3]) aroused interest not only in Japan, but also in other countries such as Romania, Hungary, Canada and the USA, where schools of Finsler geometry are founded and are presently widely recognized.

Finsler And Lagrange Geometries

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Author : Mihai Anastasiei
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Finsler And Lagrange Geometries written by Mihai Anastasiei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.

In the last decade several international conferences on Finsler, Lagrange and Hamilton geometries were organized in Bra§ov, Romania (1994), Seattle, USA (1995), Edmonton, Canada (1998), besides the Seminars that periodically are held in Japan and Romania. All these meetings produced important progress in the field and brought forth the appearance of some reference volumes. Along this line, a new International Conference on Finsler and Lagrange Geometry took place August 26-31,2001 at the "Al.I.Cuza" University in Ia§i, Romania. This Conference was organized in the framework of a Memorandum of Un derstanding (1994-2004) between the "Al.I.Cuza" University in Ia§i, Romania and the University of Alberta in Edmonton, Canada. It was especially dedicated to Prof. Dr. Peter Louis Antonelli, the liaison officer in the Memorandum, an untired promoter of Finsler, Lagrange and Hamilton geometries, very close to the Romanian School of Geometry led by Prof. Dr. Radu Miron. The dedica tion wished to mark also the 60th birthday of Prof. Dr. Peter Louis Antonelli. With this occasion a Diploma was given to Professor Dr. Peter Louis Antonelli conferring the title of Honorary Professor granted to him by the Senate of the oldest Romanian University (140 years), the "Al.I.Cuza" University, Ia§i, Roma nia. There were almost fifty participants from Egypt, Greece, Hungary, Japan, Romania, USA. There were scheduled 45 minutes lectures as well as short communications.

Dual Jet Geometrization For Time Dependent Hamiltonians And Applications

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Author : Mircea Neagu
language : en
Publisher: Springer Nature
Release Date : 2022-08-31

Dual Jet Geometrization For Time Dependent Hamiltonians And Applications written by Mircea Neagu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-31 with Mathematics categories.

This book studies a category of mathematical objects called Hamiltonians, which are dependent on both time and momenta. The authors address the development of the distinguished geometrization on dual 1-jet spaces for time-dependent Hamiltonians, in contrast with the time-independent variant on cotangent bundles. Two parts are presented to include both geometrical theory and the applicative models: Part One: Time-dependent Hamilton Geometry and Part Two: Applications to Dynamical Systems, Economy and Theoretical Physics. The authors present 1-jet spaces and their duals as appropriate fundamental ambient mathematical spaces used to model classical and quantum field theories. In addition, the authors present dual jet Hamilton geometry as a distinct metrical approach to various interdisciplinary problems.

Memoirs Of The Scientific Sections Of The Academy Of The Socialist Republic Of Romania

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Author :
language : en
Publisher:
Release Date : 2006

Memoirs Of The Scientific Sections Of The Academy Of The Socialist Republic Of Romania written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Engineering categories.

The Geometry Of Hamilton And Lagrange Spaces

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