The Hamiltonian

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An Introduction to Hamiltonian Mechanics

Gerardo F. Torres del Castillo
An Introduction to Hamiltonian Mechanics Book PDF

Author : Gerardo F. Torres del Castillo
Publisher : Springer
Page : 366 pages
File Size : 51,6 Mb
Release : 2018-09-08
Category : Mathematics
ISBN : 9783319952253

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An Introduction to Hamiltonian Mechanics by Gerardo F. Torres del Castillo Pdf

This textbook examines the Hamiltonian formulation in classical mechanics with the basic mathematical tools of multivariate calculus. It explores topics like variational symmetries, canonoid transformations, and geometrical optics that are usually omitted from an introductory classical mechanics course. For students with only a basic knowledge of mathematics and physics, this book makes those results accessible through worked-out examples and well-chosen exercises. For readers not familiar with Lagrange equations, the first chapters are devoted to the Lagrangian formalism and its applications. Later sections discuss canonical transformations, the Hamilton–Jacobi equation, and the Liouville Theorem on solutions of the Hamilton–Jacobi equation. Graduate and advanced undergraduate students in physics or mathematics who are interested in mechanics and applied math will benefit from this treatment of analytical mechanics. The text assumes the basics of classical mechanics, as well as linear algebra, differential calculus, elementary differential equations and analytic geometry. Designed for self-study, this book includes detailed examples and exercises with complete solutions, although it can also serve as a class text.

Metamorphoses of Hamiltonian Systems with Symmetries

Konstantinos Efstathiou
Metamorphoses of Hamiltonian Systems with Symmetries Book PDF

Author : Konstantinos Efstathiou
Publisher : Springer
Page : 149 pages
File Size : 54,9 Mb
Release : 2005-01-28
Category : Science
ISBN : 9783540315506

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Metamorphoses of Hamiltonian Systems with Symmetries by Konstantinos Efstathiou Pdf

Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.

Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

Kenneth R. Meyer,Daniel C. Offin
Introduction to Hamiltonian Dynamical Systems and the N Body Problem Book PDF

Author : Kenneth R. Meyer,Daniel C. Offin
Publisher : Springer
Page : 384 pages
File Size : 52,9 Mb
Release : 2017-05-04
Category : Mathematics
ISBN : 9783319536910

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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Kenneth R. Meyer,Daniel C. Offin Pdf

This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)

Introduction To Classical Mechanics

John Dirk Walecka
Introduction To Classical Mechanics Book PDF

Author : John Dirk Walecka
Publisher : World Scientific
Page : 184 pages
File Size : 41,5 Mb
Release : 2020-02-26
Category : Science
ISBN : 9789811217456

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Introduction To Classical Mechanics by John Dirk Walecka Pdf

This textbook aims to provide a clear and concise set of lectures that take one from the introduction and application of Newton's laws up to Hamilton's principle of stationary action and the lagrangian mechanics of continuous systems. An extensive set of accessible problems enhances and extends the coverage.It serves as a prequel to the author's recently published book entitled Introduction to Electricity and Magnetism based on an introductory course taught sometime ago at Stanford with over 400 students enrolled. Both lectures assume a good, concurrent, course in calculus and familiarity with basic concepts in physics; the development is otherwise self-contained.A good introduction to the subject allows one to approach the many more intermediate and advanced texts with better understanding and a deeper sense of appreciation that both students and teachers alike can share.

Multi-Hamiltonian Theory of Dynamical Systems

Maciej Blaszak
Multi Hamiltonian Theory of Dynamical Systems Book PDF

Author : Maciej Blaszak
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642588938

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Multi-Hamiltonian Theory of Dynamical Systems by Maciej Blaszak Pdf

This book offers a modern introduction to the Hamiltonian theory of dynamical systems, presenting a unified treatment of all types of dynamical systems, i.e., finite, lattice, and field. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate system. As this property is closely related to integrability, this book presents an algebraic theory of integrable.

Hamiltonian Field Theory in the Radiating Regime

Piotr T. Chrusciel,Jacek Jezierski,Jerzy Kijowski
Hamiltonian Field Theory in the Radiating Regime Book PDF

Author : Piotr T. Chrusciel,Jacek Jezierski,Jerzy Kijowski
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 42,9 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540456049

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Hamiltonian Field Theory in the Radiating Regime by Piotr T. Chrusciel,Jacek Jezierski,Jerzy Kijowski Pdf

The purpose of this monograph is to show that, in the radiation regime, there exists a Hamiltonian description of the dynamics of a massless scalar field, as well as of the dynamics of the gravitational field. The authors construct such a framework extending the previous work of Kijowski and Tulczyjew. They start by reviewing some elementary facts concerning Hamiltonian dynamical systems and then describe the geometric Hamiltonian framework, adequate for both the usual asymptotically-flat-at-spatial-infinity regime and for the radiation regime. The text then gives a detailed description of the application of the new formalism to the case of the massless scalar field. Finally, the formalism is applied to the case of Einstein gravity. The Hamiltonian role of the Trautman--Bondi mass is exhibited. A Hamiltonian definition of angular momentum at null infinity is derived and analysed.

Introduction to Hamiltonian Fluid Dynamics and Stability Theory

Gordon E Swaters
Introduction to Hamiltonian Fluid Dynamics and Stability Theory Book PDF

Author : Gordon E Swaters
Publisher : Routledge
Page : 129 pages
File Size : 40,9 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351436960

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Introduction to Hamiltonian Fluid Dynamics and Stability Theory by Gordon E Swaters Pdf

Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Until now, however, no single reference addressed and provided background in both of these closely linked subjects. Introduction to Hamiltonian Fluid Dynamics and Stability Theory does just that-offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism. The author uses the example of the nonlinear pendulum-giving a thorough linear and nonlinear stability analysis of its equilibrium solutions-to introduce many of the ideas associated with the mathematical argument required in infinite dimensional Hamiltonian theory needed for fluid mechanics. He examines Andrews' Theorem, derives and develops the Charney-Hasegawa-Mima (CMH) equation, presents an account of the Hamiltonian structure of the Korteweg-de Vries (KdV) equation, and discusses the stability theory associated with the KdV soliton. The book's tutorial approach and plentiful exercises combine with its thorough presentations of both subjects to make Introduction to Hamiltonian Fluid Dynamics and Stability Theory an ideal reference, self-study text, and upper level course book.

Integrable Hamiltonian Systems

A.V. Bolsinov,A.T. Fomenko
Integrable Hamiltonian Systems Book PDF

Author : A.V. Bolsinov,A.T. Fomenko
Publisher : CRC Press
Page : 752 pages
File Size : 52,7 Mb
Release : 2004-02-25
Category : Mathematics
ISBN : 9780203643426

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Integrable Hamiltonian Systems by A.V. Bolsinov,A.T. Fomenko Pdf

Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,

Hamiltonian and Lagrangian Flows on Center Manifolds

Alexander Mielke
Hamiltonian and Lagrangian Flows on Center Manifolds Book PDF

Author : Alexander Mielke
Publisher : Springer
Page : 145 pages
File Size : 50,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540464419

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Hamiltonian and Lagrangian Flows on Center Manifolds by Alexander Mielke Pdf

The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists, from graduate student level.

Lagrangian And Hamiltonian Mechanics: Solutions To The Exercises

Melvin G Calkin
Lagrangian And Hamiltonian Mechanics Solutions To The Exercises Book PDF

Author : Melvin G Calkin
Publisher : World Scientific Publishing Company
Page : 240 pages
File Size : 42,8 Mb
Release : 1999-03-12
Category : Science
ISBN : 9789813105416

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Lagrangian And Hamiltonian Mechanics: Solutions To The Exercises by Melvin G Calkin Pdf

This book contains the exercises from the classical mechanics text Lagrangian and Hamiltonian Mechanics, together with their complete solutions. It is intended primarily for instructors who are using Lagrangian and Hamiltonian Mechanics in their course, but it may also be used, together with that text, by those who are studying mechanics on their own.

The Hamiltonian Vision, 1789-1800

William R. Nester
The Hamiltonian Vision 1789 1800 Book PDF

Author : William R. Nester
Publisher : Potomac Books, Inc.
Page : 291 pages
File Size : 40,8 Mb
Release : 2012
Category : Biography & Autobiography
ISBN : 9781597978835

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The Hamiltonian Vision, 1789-1800 by William R. Nester Pdf

The creation of American diplomacy and power as an art

An Introduction to Hamiltonian Optics

H. A. Buchdahl
An Introduction to Hamiltonian Optics Book PDF

Author : H. A. Buchdahl
Publisher : Courier Corporation
Page : 392 pages
File Size : 44,8 Mb
Release : 1993-01-01
Category : Science
ISBN : 0486675971

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An Introduction to Hamiltonian Optics by H. A. Buchdahl Pdf

Accessible study provides detailed account of the Hamiltonian treatment of aberration theory in geometrical optics. Many classes of optical systems defined in terms of their symmetries. Detailed solutions. 1970 edition.

Summer Cannibals

Melanie Hobson
Summer Cannibals Book PDF

Author : Melanie Hobson
Publisher : Penguin
Page : 256 pages
File Size : 50,7 Mb
Release : 2018-08-21
Category : Fiction
ISBN : 9780143196396

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Summer Cannibals by Melanie Hobson Pdf

A bold and gripping literary debut about three very different sisters who return to their family home to face imminent tragedy and their tumultuous pasts. Summoned to their magnificent family home on the shores of Lake Ontario--a paradisiacal mansion perched on an escarpment above the city--three adult sisters, George, Jax, and Pippa, come together in what seems like an act of family solidarity. Pregnant and unwell, the youngest, Pippa, has left her husband and four young children in New Zealand and returned home to heal. But home to this family means secrets, desire, and vengeance--and feasting on the sexual appetites and weaknesses of others. Each daughter has her own particular taste and overlaying everything are their parents, with unquenchable desires and cravings of their own. As the affluent family endures four intense days in one another's company, old fissures reappear. When long-buried truths finally come to light, the sisters and their parents must face the unthinkable consequences of their actions. Summer Cannibals is a riveting, psychological story of lust, betrayal, and family from a dazzling new voice in Canadian fiction.

On the Splitting of Invariant Manifolds in Multidimensional Near-Integrable Hamiltonian Systems

Pierre Lochak,J.-P. Marco,D. Sauzin
On the Splitting of Invariant Manifolds in Multidimensional Near Integrable Hamiltonian Systems Book PDF

Author : Pierre Lochak,J.-P. Marco,D. Sauzin
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 51,7 Mb
Release : 2003
Category : Hamiltonian systems
ISBN : 9780821832684

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On the Splitting of Invariant Manifolds in Multidimensional Near-Integrable Hamiltonian Systems by Pierre Lochak,J.-P. Marco,D. Sauzin Pdf

Presents the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. This book offers introduction of a canonically invariant scheme for the computation of the splitting matrix.

Hamiltonian Dynamics

Gaetano Vilasi
Hamiltonian Dynamics Book PDF

Author : Gaetano Vilasi
Publisher : World Scientific
Page : 457 pages
File Size : 43,6 Mb
Release : 2001
Category : Science
ISBN : 9789810233082

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Hamiltonian Dynamics by Gaetano Vilasi Pdf

This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems.As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity.As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.