Lagrangian And Hamiltonian Dynamics
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Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds
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Author : Taeyoung Lee
language : en
Publisher: Springer
Release Date : 2017-08-14
Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds written by Taeyoung Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-14 with Mathematics categories.
This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.
Lagrangian And Hamiltonian Dynamics
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Author : Peter Mann
language : en
Publisher: Oxford University Press
Release Date : 2018
Lagrangian And Hamiltonian Dynamics written by Peter Mann and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
The book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.
Lagrangian And Hamiltonian Mechanics Solutions To The Exercises
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Author : Melvin G Calkin
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-03-12
Lagrangian And Hamiltonian Mechanics Solutions To The Exercises written by Melvin G Calkin and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-12 with Science categories.
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
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Author : Patrick Hamill
language : en
Publisher: Cambridge University Press
Release Date : 2014
A Student S Guide To Lagrangians And Hamiltonians written by Patrick Hamill 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 2014 with Mathematics categories.
A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.
Lagrangian And Hamiltonian Mechanics
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Author : Melvin G. Calkin
language : en
Publisher: World Scientific
Release Date : 1999
Lagrangian And Hamiltonian Mechanics written by Melvin G. Calkin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.
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.
Solved Problems In Lagrangian And Hamiltonian Mechanics
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Author : Claude Gignoux
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-14
Solved Problems In Lagrangian And Hamiltonian Mechanics written by Claude Gignoux 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 2009-07-14 with Science categories.
The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.
Introduction To Lagrangian Mechanics An 2nd Edition
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Author : Alain J Brizard
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-11-28
Introduction To Lagrangian Mechanics An 2nd Edition written by Alain J Brizard and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-28 with Science categories.
An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler-Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory.The Second Edition includes a larger selection of examples and problems (with hints) in each chapter and continues the strong emphasis of the First Edition on the development and application of mathematical methods (mostly calculus) to the solution of problems in Classical Mechanics.New material has been added to most chapters. For example, a new derivation of the Noether theorem for discrete Lagrangian systems is given and a modified Rutherford scattering problem is solved exactly to show that the total scattering cross section associated with a confined potential (i.e., which vanishes beyond a certain radius) yields the hard-sphere result. The Frenet-Serret formulas for the Coriolis-corrected projectile motion are presented, where the Frenet-Serret torsion is shown to be directly related to the Coriolis deflection, and a new treatment of the sleeping-top problem is given.
An Introduction To Hamiltonian Mechanics
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Author : Gerardo F. Torres del Castillo
language : en
Publisher: Springer
Release Date : 2018-09-08
An Introduction To Hamiltonian Mechanics written by Gerardo F. Torres del Castillo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-08 with Mathematics categories.
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.
New Lagrangian And Hamiltonian Methods In Field Theory
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Author : Giovanni Giachetta
language : en
Publisher: World Scientific
Release Date : 1997-12-18
New Lagrangian And Hamiltonian Methods In Field Theory written by Giovanni Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-18 with Science categories.
This book incorporates 3 modern aspects of mathematical physics: the jet methods in differential geometry, Lagrangian formalism on jet manifolds and the multimomentum approach to Hamiltonian formalism. Several contemporary field models are investigated in detail.This is not a book on differential geometry. However, modern concepts of differential geometry such as jet manifolds and connections are used throughout the book. Quadratic Lagrangians and Hamiltonians are studied at the general level including a treatment of Hamiltonian formalism on composite fiber manifolds. The book presents new geometric methods and results in field theory.
Problems In Classical And Quantum Mechanics
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Author : J. Daniel Kelley
language : en
Publisher: Springer
Release Date : 2016-11-30
Problems In Classical And Quantum Mechanics written by J. Daniel Kelley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-30 with Science categories.
This book is a collection of problems that are intended to aid students in graduate and undergraduate courses in Classical and Quantum Physics. It is also intended to be a study aid for students that are preparing for the PhD qualifying exam. Many of the included problems are of a type that could be on a qualifying exam. Others are meant to elucidate important concepts. Unlike other compilations of problems, the detailed solutions are often accompanied by discussions that reach beyond the specific problem.The solution of the problem is only the beginning of the learning process--it is by manipulation of the solution and changing of the parameters that a great deal of insight can be gleaned. The authors refer to this technique as "massaging the problem," and it is an approach that the authors feel increases the pedagogical value of any problem.