The Geometry Of Hamilton And Lagrange Spaces

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The Geometry of Hamilton and Lagrange Spaces

Author : R. Miron
Publisher : Springer Science & Business Media
ISBN 13 : 0306471353
Total Pages : 355 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis The Geometry of Hamilton and Lagrange Spaces by : R. Miron

Download or read book The Geometry of Hamilton and Lagrange Spaces written by R. Miron and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complex Spaces in Finsler, Lagrange and Hamilton Geometries

Author : Gheorghe Munteanu
Publisher : Springer Science & Business Media
ISBN 13 : 1402022069
Total Pages : 237 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Complex Spaces in Finsler, Lagrange and Hamilton Geometries by : Gheorghe Munteanu

Download or read book Complex Spaces in Finsler, Lagrange and Hamilton Geometries written by Gheorghe Munteanu and published by Springer Science & Business Media. This book was released on 2012-11-03 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

Author : Taeyoung Lee
Publisher : Springer
ISBN 13 : 3319569538
Total Pages : 561 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds by : Taeyoung Lee

Download or read book Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds written by Taeyoung Lee and published by Springer. This book was released on 2017-08-14 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.

A Student's Guide to Lagrangians and Hamiltonians

Author : Patrick Hamill
Publisher : Cambridge University Press
ISBN 13 : 1107042887
Total Pages : 185 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis A Student's Guide to Lagrangians and Hamiltonians by : Patrick Hamill

Download or read book A Student's Guide to Lagrangians and Hamiltonians written by Patrick Hamill and published by Cambridge University Press. This book was released on 2014 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.

The Geometry of Hamilton and Lagrange Spaces

Author : R. Miron
Publisher :
ISBN 13 : 9789401741736
Total Pages : 366 pages
Book Rating : 4.7/5 (417 download)

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Book Synopsis The Geometry of Hamilton and Lagrange Spaces by : R. Miron

Download or read book The Geometry of Hamilton and Lagrange Spaces written by R. Miron and published by . This book was released on 2014-03-14 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Mechanics and Symmetry

Author : Darryl D. Holm
Publisher : Oxford University Press
ISBN 13 : 0199212902
Total Pages : 537 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Geometric Mechanics and Symmetry by : Darryl D. Holm

Download or read book Geometric Mechanics and Symmetry written by Darryl D. Holm and published by Oxford University Press. This book was released on 2009-07-30 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate level text based partly on lectures in geometry, mechanics, and symmetry given at Imperial College London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the subject.

The Geometry of Higher-Order Hamilton Spaces

Author : R. Miron
Publisher : Springer Science & Business Media
ISBN 13 : 9401000700
Total Pages : 257 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis The Geometry of Higher-Order Hamilton Spaces by : R. Miron

Download or read book The Geometry of Higher-Order Hamilton Spaces written by R. Miron and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Differential Geometry

Author : Franki J.E. Dillen
Publisher : Elsevier
ISBN 13 : 0080461204
Total Pages : 575 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Handbook of Differential Geometry by : Franki J.E. Dillen

Download or read book Handbook of Differential Geometry written by Franki J.E. Dillen and published by Elsevier. This book was released on 2005-11-29 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent).All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas.. Written by experts and covering recent research. Extensive bibliography. Dealing with a diverse range of areas. Starting from the basics

Lectures on Mechanics

Author : Jerrold E. Marsden
Publisher : Cambridge University Press
ISBN 13 : 9780521428446
Total Pages : 272 pages
Book Rating : 4.4/5 (284 download)

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Book Synopsis Lectures on Mechanics by : Jerrold E. Marsden

Download or read book Lectures on Mechanics written by Jerrold E. Marsden and published by Cambridge University Press. This book was released on 1992-04-30 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the 1991 LMS Invited Lectures given by Professor Marsden, this book discusses and applies symmetry methods to such areas as bifurcations and chaos in mechanical systems.

Lectures on Symplectic Geometry

Author : Ana Cannas da Silva
Publisher : Springer
ISBN 13 : 354045330X
Total Pages : 240 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva

Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

The Convenient Setting of Global Analysis

Author : Andreas Kriegl
Publisher : American Mathematical Soc.
ISBN 13 : 0821807803
Total Pages : 631 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Convenient Setting of Global Analysis by : Andreas Kriegl

Download or read book The Convenient Setting of Global Analysis written by Andreas Kriegl and published by American Mathematical Soc.. This book was released on 1997 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR

Lagrangian and Hamiltonian Dynamics

Author : Peter Mann
Publisher : Oxford University Press
ISBN 13 : 0198822375
Total Pages : 553 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis Lagrangian and Hamiltonian Dynamics by : Peter Mann

Download or read book Lagrangian and Hamiltonian Dynamics written by Peter Mann and published by Oxford University Press. This book was released on 2018 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.

The Geometry of Lagrange Spaces: Theory and Applications

Author : R. Miron
Publisher : Springer Science & Business Media
ISBN 13 : 9401107882
Total Pages : 302 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis The Geometry of Lagrange Spaces: Theory and Applications by : R. Miron

Download or read book The Geometry of Lagrange Spaces: Theory and Applications written by R. Miron and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential-geometric methods are gaining increasing importance in the understanding of a wide range of fundamental natural phenomena. Very often, the starting point for such studies is a variational problem formulated for a convenient Lagrangian. From a formal point of view, a Lagrangian is a smooth real function defined on the total space of the tangent bundle to a manifold satisfying some regularity conditions. The main purpose of this book is to present: (a) an extensive discussion of the geometry of the total space of a vector bundle; (b) a detailed exposition of Lagrange geometry; and (c) a description of the most important applications. New methods are described for construction geometrical models for applications. The various chapters consider topics such as fibre and vector bundles, the Einstein equations, generalized Einstein--Yang--Mills equations, the geometry of the total space of a tangent bundle, Finsler and Lagrange spaces, relativistic geometrical optics, and the geometry of time-dependent Lagrangians. Prerequisites for using the book are a good foundation in general manifold theory and a general background in geometrical models in physics. For mathematical physicists and applied mathematicians interested in the theory and applications of differential-geometric methods.

New Lagrangian And Hamiltonian Methods In Field Theory

Author : Giovanni Giachetta
Publisher : World Scientific
ISBN 13 : 9814518085
Total Pages : 466 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis New Lagrangian And Hamiltonian Methods In Field Theory by : Giovanni Giachetta

Download or read book New Lagrangian And Hamiltonian Methods In Field Theory written by Giovanni Giachetta and published by World Scientific. This book was released on 1997-12-18 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book incorporates 3 modern aspects of mathematical physics: the jet methods in differential geometry, Lagrangian formalism on jet manifolds and the multimomentum approach to Hamiltonian formalism. Several contemporary field models are investigated in detail.This is not a book on differential geometry. However, modern concepts of differential geometry such as jet manifolds and connections are used throughout the book. Quadratic Lagrangians and Hamiltonians are studied at the general level including a treatment of Hamiltonian formalism on composite fiber manifolds. The book presents new geometric methods and results in field theory.

Generalized Hamiltonian Formalism for Field Theory

Author : G. Sardanashvily
Publisher : World Scientific
ISBN 13 : 9789810220457
Total Pages : 168 pages
Book Rating : 4.2/5 (24 download)

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Book Synopsis Generalized Hamiltonian Formalism for Field Theory by : G. Sardanashvily

Download or read book Generalized Hamiltonian Formalism for Field Theory written by G. Sardanashvily and published by World Scientific. This book was released on 1995 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the framework of the geometric formulation of field theory, classical fields are represented by sections of fibred manifolds, and their dynamics is phrased in jet manifold terms. The Hamiltonian formalism in fibred manifolds is the multisymplectic generalization of the Hamiltonian formalism in mechanics when canonical momenta correspond to derivatives of fields with respect to all world coordinates, not only to time. This book is devoted to the application of this formalism to fundamental field models including gauge theory, gravitation theory, and spontaneous symmetry breaking. All these models are constraint ones. Their Euler-Lagrange equations are underdetermined and need additional conditions. In the Hamiltonian formalism, these conditions appear automatically as a part of the Hamilton equations, corresponding to different Hamiltonian forms associated with a degenerate Lagrangian density. The general procedure for describing constraint systems with quadratic and affine Lagrangian densities is presented.

Classical Mechanics

Author : Alexei Deriglazov
Publisher : Springer Science & Business Media
ISBN 13 : 3642140378
Total Pages : 317 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Classical Mechanics by : Alexei Deriglazov

Download or read book Classical Mechanics written by Alexei Deriglazov and published by Springer Science & Business Media. This book was released on 2010-08-28 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, as well as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. The mathematical constructions involved are explicitly described and explained, so the book can be a good starting point for the undergraduate student new to this field. At the same time and where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for the graduate students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.

Symplectic Geometry and Analytical Mechanics

Author : P. Libermann
Publisher : Springer Science & Business Media
ISBN 13 : 9400938071
Total Pages : 541 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Symplectic Geometry and Analytical Mechanics by : P. Libermann

Download or read book Symplectic Geometry and Analytical Mechanics written by P. Libermann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. and begin with the answers. Then one day, It is that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' Brown 'The point of a Pin'. in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thouglit to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sci ences has changed drastically in recent years: measure theory is used (non-trivially) in re gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homo topy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.