The Geometry Of Ordinary Variational Equations

DOWNLOAD

Download The Geometry Of Ordinary Variational Equations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Geometry Of Ordinary Variational Equations book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

The Geometry Of Ordinary Variational Equations

DOWNLOAD
Author : Olga Krupkova
language : en
Publisher: Springer
Release Date : 2006-11-14

The Geometry Of Ordinary Variational Equations written by Olga Krupkova and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

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.

Introduction To Global Variational Geometry

DOWNLOAD
Author : Demeter Krupka
language : en
Publisher: Elsevier
Release Date : 2000-04-01

Introduction To Global Variational Geometry written by Demeter Krupka and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether’s theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces

Variational Principles For Second Order Differential Equations Application Of The Spencer Theory Of

DOWNLOAD
Author : Joseph Grifone
language : en
Publisher: World Scientific
Release Date : 2000-05-25

Variational Principles For Second Order Differential Equations Application Of The Spencer Theory Of written by Joseph Grifone and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-25 with Mathematics categories.

The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric.To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc.

Variational Principles For Second Order Differential Equations

DOWNLOAD
Author : J. Grifone
language : en
Publisher: World Scientific
Release Date : 2000

Variational Principles For Second Order Differential Equations written by J. Grifone and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric.To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc.

Harmonic Maps And Minimal Immersions With Symmetries Am 130 Volume 130

DOWNLOAD
Author : James Eells
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02

Harmonic Maps And Minimal Immersions With Symmetries Am 130 Volume 130 written by James Eells and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.

The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Non Commuting Variations In Mathematics And Physics

DOWNLOAD
Author : Serge Preston
language : en
Publisher: Springer
Release Date : 2016-03-02

Non Commuting Variations In Mathematics And Physics written by Serge Preston and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Technology & Engineering categories.

This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equations with dissipation and corresponding s balance laws is presented.

Harmonic Maps And Minimal Immersions With Symmetries

DOWNLOAD
Author : James Eells
language : en
Publisher: Princeton University Press
Release Date : 1993

Harmonic Maps And Minimal Immersions With Symmetries written by James Eells and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Variational Topological And Partial Order Methods With Their Applications

DOWNLOAD
Author : Zhitao Zhang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-17

Variational Topological And Partial Order Methods With Their Applications written by Zhitao Zhang 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 2012-09-17 with Mathematics categories.

Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.

Variational Problems In Riemannian Geometry

DOWNLOAD
Author : Paul Baird
language : en
Publisher: Birkhäuser
Release Date : 2012-11-01

Variational Problems In Riemannian Geometry written by Paul Baird and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-01 with Mathematics categories.

This volume has grown from a conference entitled Harmonic Maps, Minimal Sur faces and Geometric Flows which was held at the Universite de Bretagne Occi dentale from July 7th-12th, 2002, in the town of Brest in Brittany, France. We welcomed many distinguished mathematicians from around the world and a dy namic meeting took place, with many fruitful exchanges of ideas. In order to produce a work that would have lasting value to the mathematical community, the organisers decided to invite a small number of participants to write in-depth articles around a common theme. These articles provide a balance between introductory surveys and ones that present the newest results that lie at the frontiers of research. We thank these mathematicians, all experts in their field, for their contributions. Such meetings depend on the support of national organisations and the local community and we would like to thank the following: the Ministere de l'Education Nationale, Ministere des Affaires Etrangeres, Centre National de Recherche Sci en tifique (CNRS), Conseil Regional de Bretagne, Conseil General du Finistere, Com munaute Urbaine de Brest, Universite de Bretagne Occidentale (UBO), Faculte des Sciences de l'UBO, Laboratoire de Mathematiques de l'UBO and the Departement de Mathematiques de l'UBO. Their support was generous and ensured the success of the meeting. We would also like to thank the members of the scientific committee for their advice and for their participation in the conception and composition of this volume: Pierre Berard, Jean-Pierre Bourguignon, Frederic Helein, Seiki Nishikawa and Franz Pedit.

Variational Methods In Lorentzian Geometry

DOWNLOAD
Author : Antonio Masiello
language : en
Publisher: Routledge
Release Date : 2017-10-05

Variational Methods In Lorentzian Geometry written by Antonio Masiello and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-05 with Mathematics categories.

Appliies variational methods and critical point theory on infinite dimenstional manifolds to some problems in Lorentzian geometry which have a variational nature, such as existence and multiplicity results on geodesics and relations between such geodesics and the topology of the manifold.