Discrete Hamiltonian Systems
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Discrete Hamiltonian Systems
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Author : Calvin Ahlbrandt
language : en
Publisher: Springer
Release Date : 1996-10-31
Discrete Hamiltonian Systems written by Calvin Ahlbrandt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-31 with Mathematics categories.
This book should be accessible to students who have had a first course in matrix theory. The existence and uniqueness theorem of Chapter 4 requires the implicit function theorem, but we give a self-contained constructive proof ofthat theorem. The reader willing to accept the implicit function theorem can read the book without an advanced calculus background. Chapter 8 uses the Moore-Penrose pseudo-inverse, but is accessible to students who have facility with matrices. Exercises are placed at those points in the text where they are relevant. For U. S. universities, we intend for the book to be used at the senior undergraduate level or beginning graduate level. Chapter 2, which is on continued fractions, is not essential to the material of the remaining chapters, but is intimately related to the remaining material. Continued fractions provide closed form representations of the extreme solutions of some discrete matrix Riccati equations. Continued fractions solution methods for Riccati difference equations provide an approach analogous to series solution methods for linear differential equations. The book develops several topics which have not been available at this level. In particular, the material of the chapters on continued fractions (Chapter 2), symplectic systems (Chapter 3), and discrete variational theory (Chapter 4) summarize recent literature. Similarly, the material on transforming Riccati equations presented in Chapter 3 gives a self-contained unification of various forms of Riccati equations. Motivation for our approach to difference equations came from the work of Harris, Vaughan, Hartman, Reid, Patula, Hooker, Erbe & Van, and Bohner.
Discrete Hamiltonian Systems
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Author : Calvin Ahlbrandt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Discrete Hamiltonian Systems written by Calvin Ahlbrandt 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 2013-06-29 with Mathematics categories.
This book should be accessible to students who have had a first course in matrix theory. The existence and uniqueness theorem of Chapter 4 requires the implicit function theorem, but we give a self-contained constructive proof ofthat theorem. The reader willing to accept the implicit function theorem can read the book without an advanced calculus background. Chapter 8 uses the Moore-Penrose pseudo-inverse, but is accessible to students who have facility with matrices. Exercises are placed at those points in the text where they are relevant. For U. S. universities, we intend for the book to be used at the senior undergraduate level or beginning graduate level. Chapter 2, which is on continued fractions, is not essential to the material of the remaining chapters, but is intimately related to the remaining material. Continued fractions provide closed form representations of the extreme solutions of some discrete matrix Riccati equations. Continued fractions solution methods for Riccati difference equations provide an approach analogous to series solution methods for linear differential equations. The book develops several topics which have not been available at this level. In particular, the material of the chapters on continued fractions (Chapter 2), symplectic systems (Chapter 3), and discrete variational theory (Chapter 4) summarize recent literature. Similarly, the material on transforming Riccati equations presented in Chapter 3 gives a self-contained unification of various forms of Riccati equations. Motivation for our approach to difference equations came from the work of Harris, Vaughan, Hartman, Reid, Patula, Hooker, Erbe & Van, and Bohner.
Construction Of Mappings For Hamiltonian Systems And Their Applications
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Author : Sadrilla S. Abdullaev
language : en
Publisher: Springer
Release Date : 2006-08-02
Construction Of Mappings For Hamiltonian Systems And Their Applications written by Sadrilla S. Abdullaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-02 with Science categories.
Based on the method of canonical transformation of variables and the classical perturbation theory, this innovative book treats the systematic theory of symplectic mappings for Hamiltonian systems and its application to the study of the dynamics and chaos of various physical problems described by Hamiltonian systems. It develops a new, mathematically-rigorous method to construct symplectic mappings which replaces the dynamics of continuous Hamiltonian systems by the discrete ones. Applications of the mapping methods encompass the chaos theory in non-twist and non-smooth dynamical systems, the structure and chaotic transport in the stochastic layer, the magnetic field lines in magnetically confinement devices of plasmas, ray dynamics in waveguides, etc. The book is intended for postgraduate students and researches, physicists and astronomers working in the areas of plasma physics, hydrodynamics, celestial mechanics, dynamical astronomy, and accelerator physics. It should also be useful for applied mathematicians involved in analytical and numerical studies of dynamical systems.
Nonlinear H Infinity Control Hamiltonian Systems And Hamilton Jacobi Equations
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Author : M.D.S. Aliyu
language : en
Publisher: CRC Press
Release Date : 2011-02-11
Nonlinear H Infinity Control Hamiltonian Systems And Hamilton Jacobi Equations written by M.D.S. Aliyu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-11 with Mathematics categories.
A comprehensive overview of nonlinear H∞ control theory for both continuous-time and discrete-time systems, Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H∞-control, nonlinear H∞ -filtering, mixed H2/ H∞-nonlinear control and filtering, nonlinear H∞-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter. Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE) has facilitated the application of Hamilton-Jacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H∞-control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography. Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.
Introduction To The Perturbation Theory Of Hamiltonian Systems
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Author : Dmitry Treschev
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-08
Introduction To The Perturbation Theory Of Hamiltonian Systems written by Dmitry Treschev 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 2009-10-08 with Mathematics categories.
This book is an extended version of lectures given by the ?rst author in 1995–1996 at the Department of Mechanics and Mathematics of Moscow State University. We believe that a major part of the book can be regarded as an additional material to the standard course of Hamiltonian mechanics. In comparison with the original Russian 1 version we have included new material, simpli?ed some proofs and corrected m- prints. Hamiltonian equations ?rst appeared in connection with problems of geometric optics and celestial mechanics. Later it became clear that these equations describe a large classof systemsin classical mechanics,physics,chemistry,and otherdomains. Hamiltonian systems and their discrete analogs play a basic role in such problems as rigid body dynamics, geodesics on Riemann surfaces, quasi-classic approximation in quantum mechanics, cosmological models, dynamics of particles in an accel- ator, billiards and other systems with elastic re?ections, many in?nite-dimensional models in mathematical physics, etc. In this book we study Hamiltonian systems assuming that they depend on some parameter (usually?), where for?= 0 the dynamics is in a sense simple (as a rule, integrable). Frequently such a parameter appears naturally. For example, in celestial mechanics it is accepted to take? equal to the ratio: the mass of Jupiter over the mass of the Sun. In other cases it is possible to introduce the small parameter ar- ?cially.
Discrete Hamiltonian Systems
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Author : Douglas R. Anderson
language : en
Publisher:
Release Date : 1997
Discrete Hamiltonian Systems written by Douglas R. Anderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Discrete And Continuous Nonlinear Schr Dinger Systems
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Author : M. J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 2004
Discrete And Continuous Nonlinear Schr Dinger Systems written by M. J. Ablowitz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such 'soliton equations'. The IST technique applies to both continuous and discrete nonlinear Schrödinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book, first published in 2003, presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the previously-published literature.
Mechanics From Theory To Computation
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Author : Juan Carlos Simo
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Mechanics From Theory To Computation written by Juan Carlos Simo 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 2000 with Mathematics categories.
This collection of papers in honour of Juan-Carlos Simo cover subjects including: dynamical problems for geometrically exact theories of nonlinearly viscoelastic rods; gravity waves on the surface of the sphere; and problems and progress in microswimming.
Mechanics From Theory To Computation
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Author : Journal of Nonlinear Science
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mechanics From Theory To Computation written by Journal of Nonlinear Science 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 Science categories.
Starting in 1996, a sequence of articles appeared in the Journal of Nonlinear Science dedicated to the memory of one of its original editors, Juan-Carlos Simo, Applied Me chanics, Stanford University. Sadly, Juan-Carlos passed away at an early age in 1994. We lost a brilliant colleague and a wonderful person. These articles are collected in the present volume. Many of them are updated and corrected especially for this occasion. These essays are in areas of scientific interest of Juan-Carlos, including mechanics (particles, rigid bodies, fluids, elasticity, plastic ity, etc.), geometry, applied dynamics, and, of course, computation. His interests were extremely broad-he did not see boundaries between computation, mathematics, me chanics, and dynamics, and, in that sense, he ideally reflected the spirit of the journal and many of the most exciting areas of current scientific interest. Juan-Carlos was one of those select and gifted people who could cross interdisci plinary boundaries with extremely high quality and productive interactions of lasting value. His contributions, ranging from concrete engineering problems to fundamental mathematical theorems in geometric mechanics, are remarkable. In current conferences as well as in scientific books and articles, and over a wide range of subjects, one frequently hears how his ideas as well as specific results are often used and quoted-this is one indication of just how profound and fundamental his work has impacted the community.
Symplectic Difference Systems Oscillation And Spectral Theory
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Author : Ondřej Došlý
language : en
Publisher: Springer Nature
Release Date : 2019-09-06
Symplectic Difference Systems Oscillation And Spectral Theory written by Ondřej Došlý and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-06 with Mathematics categories.
This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics.