Hamiltonian Mechanics

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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 : 41,5 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.

Hamiltonian Dynamics

Gaetano Vilasi
Hamiltonian Dynamics Book PDF

Author : Gaetano Vilasi
Publisher : World Scientific
Page : 457 pages
File Size : 43,7 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.

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 : 50,6 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.

A Student's Guide to Lagrangians and Hamiltonians

Patrick Hamill
A Student s Guide to Lagrangians and Hamiltonians Book PDF

Author : Patrick Hamill
Publisher : Cambridge University Press
Page : 185 pages
File Size : 42,9 Mb
Release : 2014
Category : Mathematics
ISBN : 9781107042889

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A Student's Guide to Lagrangians and Hamiltonians by Patrick Hamill Pdf

A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.

Introduction to Classical Mechanics

David Morin
Introduction to Classical Mechanics Book PDF

Author : David Morin
Publisher : Cambridge University Press
Page : 713 pages
File Size : 45,6 Mb
Release : 2008-01-10
Category : Science
ISBN : 9781139468374

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Introduction to Classical Mechanics by David Morin Pdf

This textbook covers all the standard introductory topics in classical mechanics, including Newton's laws, oscillations, energy, momentum, angular momentum, planetary motion, and special relativity. It also explores more advanced topics, such as normal modes, the Lagrangian method, gyroscopic motion, fictitious forces, 4-vectors, and general relativity. It contains more than 250 problems with detailed solutions so students can easily check their understanding of the topic. There are also over 350 unworked exercises which are ideal for homework assignments. Password protected solutions are available to instructors at www.cambridge.org/9780521876223. The vast number of problems alone makes it an ideal supplementary text for all levels of undergraduate physics courses in classical mechanics. Remarks are scattered throughout the text, discussing issues that are often glossed over in other textbooks, and it is thoroughly illustrated with more than 600 figures to help demonstrate key concepts.

Convexity Methods in Hamiltonian Mechanics

Ivar Ekeland
Convexity Methods in Hamiltonian Mechanics Book PDF

Author : Ivar Ekeland
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642743313

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Convexity Methods in Hamiltonian Mechanics by Ivar Ekeland Pdf

In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the three-body problem in celestial mechanics, they are found by perturbation theory: there is a small parameter € in the problem, the mass of the perturbing body for instance, and for € = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for € -# 0 small enough. Poincare also introduced global methods, relying on the topological properties of the flow, and the fact that it preserves the 2-form L~=l dPi 1\ dqi' The most celebrated result he obtained in this direction is his last geometric theorem, which states that an area-preserving map of the annulus which rotates the inner circle and the outer circle in opposite directions must have two fixed points. And now another ancient theme appear: the least action principle. It states that the periodic solutions of a Hamiltonian system are extremals of a suitable integral over closed curves. In other words, the problem is variational. This fact was known to Fermat, and Maupertuis put it in the Hamiltonian formalism. In spite of its great aesthetic appeal, the least action principle has had little impact in Hamiltonian mechanics. There is, of course, one exception, Emmy Noether's theorem, which relates integrals ofthe motion to symmetries of the equations. But until recently, no periodic solution had ever been found by variational methods.

Classical Mechanics

Walter Greiner
Classical Mechanics Book PDF

Author : Walter Greiner
Publisher : Springer Science & Business Media
Page : 574 pages
File Size : 44,8 Mb
Release : 2009-11-13
Category : Science
ISBN : 9783642034343

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Classical Mechanics by Walter Greiner Pdf

The series of texts on Classical Theoretical Physics is based on the highly successful courses given by Walter Greiner. The volumes provide a complete survey of classical theoretical physics and an enormous number of worked out examples and problems.

Hamiltonian Mechanics of Gauge Systems

Lev V. Prokhorov,Sergei V. Shabanov
Hamiltonian Mechanics of Gauge Systems Book PDF

Author : Lev V. Prokhorov,Sergei V. Shabanov
Publisher : Cambridge University Press
Page : 485 pages
File Size : 44,6 Mb
Release : 2011-09-22
Category : Science
ISBN : 9781139500906

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Hamiltonian Mechanics of Gauge Systems by Lev V. Prokhorov,Sergei V. Shabanov Pdf

The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.

Mathematical Methods of Classical Mechanics

V.I. Arnol'd
Mathematical Methods of Classical Mechanics Book PDF

Author : V.I. Arnol'd
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 47,6 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9781475720631

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Mathematical Methods of Classical Mechanics by V.I. Arnol'd Pdf

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Hamiltonian Mechanical Systems and Geometric Quantization

Mircea Puta
Hamiltonian Mechanical Systems and Geometric Quantization Book PDF

Author : Mircea Puta
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401119924

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Hamiltonian Mechanical Systems and Geometric Quantization by Mircea Puta Pdf

This volume presents various aspects of the geometry of symplectic and Poisson manifolds, and applications in Hamiltonian mechanics and geometric quantization are indicated. Chapter 1 presents some general facts about symplectic vector space, symplectic manifolds and symplectic reduction. Chapter 2 deals with the study of Hamiltonian mechanics. Chapter 3 considers some standard facts concerning Lie groups and algebras which lead to the theory of momentum mappings and the Marsden--Weinstein reduction. Chapters 4 and 5 consider the theory and the stability of equilibrium solutions of Hamilton--Poisson mechanical systems. Chapters 6 and 7 are devoted to the theory of geometric quantization. This leads, in Chapter 8, to topics such as foliated cohomology, the theory of the Dolbeault--Kostant complex, and their applications. A discussion of the relation between geometric quantization and the Marsden--Weinstein reduction is presented in Chapter 9. The final chapter considers extending the theory of geometric quantization to Poisson manifolds, via the theory of symplectic groupoids. Each chapter concludes with problems and solutions, many of which present significant applications and, in some cases, major theorems. For graduate students and researchers whose interests and work involve symplectic geometry and Hamiltonian mechanics.

Classical Mechanics

Alexei Deriglazov
Classical Mechanics Book PDF

Author : Alexei Deriglazov
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 45,6 Mb
Release : 2010-08-28
Category : Science
ISBN : 9783642140372

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Classical Mechanics by Alexei Deriglazov Pdf

Formalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, as well as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. The mathematical constructions involved are explicitly described and explained, so the book can be a good starting point for the undergraduate student new to this field. At the same time and where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for the graduate students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.

Lagrangian and Hamiltonian Dynamics

Peter Mann
Lagrangian and Hamiltonian Dynamics Book PDF

Author : Peter Mann
Publisher : Oxford University Press
Page : 553 pages
File Size : 46,7 Mb
Release : 2018
Category : Mathematics
ISBN : 9780198822370

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Lagrangian and Hamiltonian Dynamics by Peter Mann Pdf

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the 'classical wavefunction', Koopman-von Neumann theory, classical density functional theories, the 'vakonomic' variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.

Simulating Hamiltonian Dynamics

Benedict Leimkuhler,Sebastian Reich
Simulating Hamiltonian Dynamics Book PDF

Author : Benedict Leimkuhler,Sebastian Reich
Publisher : Cambridge University Press
Page : 464 pages
File Size : 51,9 Mb
Release : 2004
Category : Mathematics
ISBN : 0521772907

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Simulating Hamiltonian Dynamics by Benedict Leimkuhler,Sebastian Reich Pdf

Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.

Structure and Interpretation of Classical Mechanics, second edition

Gerald Jay Sussman,Jack Wisdom
Structure and Interpretation of Classical Mechanics second edition Book PDF

Author : Gerald Jay Sussman,Jack Wisdom
Publisher : MIT Press
Page : 580 pages
File Size : 41,8 Mb
Release : 2015-02-06
Category : Science
ISBN : 9780262028967

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Structure and Interpretation of Classical Mechanics, second edition by Gerald Jay Sussman,Jack Wisdom Pdf

The new edition of a classic text that concentrates on developing general methods for studying the behavior of classical systems, with extensive use of computation. We now know that there is much more to classical mechanics than previously suspected. Derivations of the equations of motion, the focus of traditional presentations of mechanics, are just the beginning. This innovative textbook, now in its second edition, concentrates on developing general methods for studying the behavior of classical systems, whether or not they have a symbolic solution. It focuses on the phenomenon of motion and makes extensive use of computer simulation in its explorations of the topic. It weaves recent discoveries in nonlinear dynamics throughout the text, rather than presenting them as an afterthought. Explorations of phenomena such as the transition to chaos, nonlinear resonances, and resonance overlap to help the student develop appropriate analytic tools for understanding. The book uses computation to constrain notation, to capture and formalize methods, and for simulation and symbolic analysis. The requirement that the computer be able to interpret any expression provides the student with strict and immediate feedback about whether an expression is correctly formulated. This second edition has been updated throughout, with revisions that reflect insights gained by the authors from using the text every year at MIT. In addition, because of substantial software improvements, this edition provides algebraic proofs of more generality than those in the previous edition; this improvement permeates the new edition.

Lagrangian and Hamiltonian Mechanics

Melvin G. Calkin
Lagrangian and Hamiltonian Mechanics Book PDF

Author : Melvin G. Calkin
Publisher : World Scientific
Page : 244 pages
File Size : 48,8 Mb
Release : 1999
Category : Science
ISBN : 9810237820

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Lagrangian and Hamiltonian Mechanics 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.