The Inverse Problem Of The Calculus Of Variations For Ordinary Differential Equations

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The Inverse Problem Of The Calculus Of Variations For Ordinary Differential Equations

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Author : Ian Anderson
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

The Inverse Problem Of The Calculus Of Variations For Ordinary Differential Equations written by Ian Anderson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centres on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coicides with a given system of ordinary differential equations. The authors rederive the basic necessary and sufficient conditions of Douglas for second order equations and extend them to equations of higher order using methods of the variational bicomplex of Tulcyjew, Vinogradov, and Tsujishita. The authors present an algorithm, based upon exterior differential systems techniques, for solving the inverse problem for second order equations. a number of new examples illustrate the effectiveness of this approach.

The Inverse Problem Of The Calculus Of Variations

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Author : Dmitry V. Zenkov
language : en
Publisher: Springer
Release Date : 2015-10-15

The Inverse Problem Of The Calculus Of Variations written by Dmitry V. Zenkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-15 with Mathematics categories.

The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).

New Prospects In Direct Inverse And Control Problems For Evolution Equations

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Author : Angelo Favini
language : en
Publisher: Springer
Release Date : 2014-11-27

New Prospects In Direct Inverse And Control Problems For Evolution Equations written by Angelo Favini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Mathematics categories.

This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.

Finslerian Geometries

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Author : P.L. Antonelli
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Finslerian Geometries written by P.L. Antonelli 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.

The International Conference on Finsler and Lagrange Geometry and its Applications: A Meeting of Minds, took place August 13-20, 1998 at the University of Alberta in Edmonton, Canada. The main objective of this meeting was to help acquaint North American geometers with the extensive modern literature on Finsler geometry and Lagrange geometry of the Japanese and European schools, each with its own venerable history, on the one hand, and to communicate recent advances in stochastic theory and Hodge theory for Finsler manifolds by the younger North American school, on the other. The intent was to bring together practitioners of these schools of thought in a Canadian venue where there would be ample opportunity to exchange information and have cordial personal interactions. The present set of refereed papers begins ·with the Pedagogical Sec tion I, where introductory and brief survey articles are presented, one from the Japanese School and two from the European School (Romania and Hungary). These have been prepared for non-experts with the intent of explaining basic points of view. The Section III is the main body of work. It is arranged in alphabetical order, by author. Section II gives a brief account of each of these contribu tions with a short reference list at the end. More extensive references are given in the individual articles.

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

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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

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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.

Handbook Of Global Analysis

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Author : Demeter Krupka
language : en
Publisher: Elsevier
Release Date : 2011-08-11

Handbook Of Global Analysis 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 2011-08-11 with Mathematics categories.

This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents

Selected Topics In The Geometrical Study Of Differential Equations

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Author : Niky Kamran
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-01-01

Selected Topics In The Geometrical Study Of Differential Equations written by Niky Kamran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.

The geometrical study of differential equations has a long and distinguished history, dating back to the classical investigations of Sophus Lie, Gaston Darboux, and Elie Cartan. Currently, these ideas occupy a central position in several areas of pure and applied mathematics. In this book, the author gives an overview of a number of significant ideas and results developed over the past decade in the geometrical study of differential equations. Topics covered in the book include symmetries of differential equations and variational problems, the variational bi-complex and conservation laws, geom.

Lie Groups Differential Equations And Geometry

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Author : Giovanni Falcone
language : en
Publisher: Springer
Release Date : 2017-09-19

Lie Groups Differential Equations And Geometry written by Giovanni Falcone and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-19 with Mathematics categories.

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.

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Author : V. M. Filippov
language : en
Publisher: American Mathematical Soc.
Release Date : 1989-12-31

written by V. M. Filippov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-12-31 with Mathematics categories.

This book develops a variational method for solving linear equations with $B$-symmetric and $B$-positive operators and generalizes the method to nonlinear equations with nonpotential operators. The author carries out a constructive extension of the variational method to ``nonvariational'' equations (including parabolic equations) in classes of functionals which differ from the Euler-Lagrange functionals. In this connection, some new functions spaces are considered. Intended for mathematicians working in the areas of functional analysis and differential equations, this book would also prove useful for researchers in other areas and students in advanced courses who use variational methods in solving linear and nonlinear boundary value problems in continuum mechanics and theoretical physics.