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.
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:
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.
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.
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 539 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.
Download or read book The Geometry of Lagrange Spaces written by R. Miron and published by . This book was released on 2014-01-15 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book The Geometry of Ordinary Variational Equations written by Olga Krupkova and published by Springer. This book was released on 2006-11-14 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations.
Download or read book New Lagrangian and Hamiltonian Methods in Field Theory written by G. Giachetta and published by World Scientific. This book was released on 1997 with total page 472 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.
Download or read book The Geometry of Lagrange Spaces Theory and Applications written by R. Miron and published by Springer. This book was released on 1994 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an extensive discussion of the geometry of the total space of a vector bundle, a detailed exposition of Lagrange geometry, and a description of the most important applications. Describes new methods for construction of geometrical models for applications. Topics include fiber and vector bundles, generalized Einstein-Yang-Mills equations, Finsler and Lagrange spaces, relativistic geometrical optics, and the geometry of time- dependent Lagrangians. Annotation copyright by Book News, Inc., Portland, OR
Download or read book The Geometry of Higher Order Hamilton Spaces written by R. Miron and published by . This book was released on 2014-01-15 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Methods of Differential Geometry in Classical Field Theories written by Manuel de León and published by World Scientific. This book was released on 2015-10-21 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to review two of the most relevant approaches to the study of classical field theories of the first order, say k-symplectic and k-cosymplectic geometry. This approach is also compared with others like multisymplectic formalism. It will be very useful for researchers working in classical field theories and graduate students interested in developing a scientific career in the subject. Contents:A Review of Hamiltonian and Lagrangian Mechanics:Hamiltonian and Lagrangian Mechanicsk-Symplectic Formulation of Classical Field Theories:k-Symplectic Geometryk-Symplectic FormalismHamiltonian Classical Field TheoryHamilton–Jacobi Theory in k-Symplectic Field TheoriesLagrangian Classical Field TheoriesExamplesk-Cosymplectic Formulation of Classical Field Theories:k-Cosymplectic Geometryk-Cosymplectic FormalismHamiltonian Classical Field TheoriesHamilton–Jacobi EquationLagrangian Classical Field TheoriesExamplesk-Symplectic Systems versus Autonomous k-Cosymplectic SystemsRelationship between k-Symplectic and k-Cosymplectic Approaches and the Multisymplectic Formalism:Multisymplectic FormalismAppendices:Symplectic ManifoldsCosymplectic ManifoldsGlossary of Symbols Readership: Graduate students and researchers in classical field theories. Key Features:This book contains for the first time this new geometric approach to Classical Field Theory. Up to now the theory is disseminated in several journal papersThe subject is very active in the last yearsThere are many open problems in Classical Field Theories to be attacked using this new formalismKeywords:Classical Field Theory;k-Symplectic;k-Cosymplectic;Multisymplectic Formalism
Download or read book Geometric Mechanics on Riemannian Manifolds written by Ovidiu Calin and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: * A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics
Download or read book Finsler and Lagrange Geometries written by Mihai Anastasiei and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 574 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
Download or read book Mechanics in Differential Geometry written by Yves Talpaert and published by Walter de Gruyter. This book was released on 2012-03-20 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
