The Geometry Of Higher Order Hamilton Spaces
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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
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 2012-12-06 with Mathematics categories.
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 Hamilton Spaces
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Author : R. Miron
language : en
Publisher:
Release Date : 2014-01-15
The Geometry Of Higher Order Hamilton 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 2014-01-15 with categories.
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 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 2006-04-11 with Mathematics categories.
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 Lagrange Spaces
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Author : R. Miron
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-31
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 1997-01-31 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.
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.
Handbook Of Differential Geometry
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Author : Franki J.E. Dillen
language : en
Publisher: Elsevier
Release Date : 2005-11-29
Handbook Of Differential Geometry written by Franki J.E. Dillen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-29 with Mathematics categories.
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
Challenges To The Second Law Of Thermodynamics
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Author : Vladislav Capek
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-02-15
Challenges To The Second Law Of Thermodynamics written by Vladislav Capek 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 2005-02-15 with Philosophy categories.
The second law of thermodynamics is considered one of the central laws of science, engineering and technology. For over a century it has been assumed to be inviolable by the scientific community. Over the last 10-20 years, however, more than two dozen challenges to it have appeared in the physical literature - more than during any other period in its 150-year history. The number and variety of these represent a cogent threat to its absolute status. This is the first book to document and critique these modern challenges. Written by two leading exponents of this rapidly emerging field, it covers the theoretical and experimental aspects of principal challenges. In addition, unresolved foundational issues concerning entropy and the second law are explored. This book should be of interest to anyone whose work or research is touched by the second law.
Lagrangian And Hamiltonian Geometries Applications To Mechanics
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Author : Miron Radu
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2015-06-08
Lagrangian And Hamiltonian Geometries Applications To Mechanics written by Miron Radu and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-08 with categories.
The purpose of this book is to provide a presentation of the geometrical theory of Lagrange and Hamilton spaces of order k, greater or equal to 1, as well as to define and investigate some new Analytical Mechanics. It is shown that a rigorous geometrical theory of conservative and non-conservative mechanical systems can be raised based on the Lagrangian and Hamiltonian geometries. And that these geometries relies on the mechanical principles. The book covers the following topics: Lagrange and Hamilton spaces; Lagrange and Hamilton spaces of higher order; Analytical Mechanics of Lagrangian and Hamiltonian mechanical systems. The novelty consists of the following: a geometrization of the classical non-conservative mechanical systems, whose external forces depend on velocities, the notion of Finslerian mechanical system, the definition of Cartan mechanical system, a theory of Lagrangian and Hamiltonian mechanical systems by means of the geometry of tangent (cotangent) bundle, the geometrization of the higher order Lagrangian and Hamiltonian mechanical systems, fundamental equations of Riemannian mechanical systems whose external forces depend on higher order accelerations.
Libertas Mathematica
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Author :
language : en
Publisher:
Release Date : 2002
Libertas Mathematica written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Introduction To Soliton Theory Applications To Mechanics
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Author : Ligia Munteanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-06
Introduction To Soliton Theory Applications To Mechanics written by Ligia 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 2006-07-06 with Mathematics categories.
This monograph is planned to provide the application of the soliton theory to solve certain practical problems selected from the fields of solid mechanics, fluid mechanics and biomechanics. The work is based mainly on the authors’ research carried out at their home institutes, and on some specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Éd. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses.