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Analytical Mechanics

Analytical Mechanics Book
Author : Louis N. Hand,Janet D. Finch
Publisher : Cambridge University Press
Release : 1998-11-13
ISBN : 1139643312
Language : En, Es, Fr & De

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Book Description :

Analytical Mechanics, first published in 1999, provides a detailed introduction to the key analytical techniques of classical mechanics, one of the cornerstones of physics. It deals with all the important subjects encountered in an undergraduate course and prepares the reader thoroughly for further study at graduate level. The authors set out the fundamentals of Lagrangian and Hamiltonian mechanics early on in the book and go on to cover such topics as linear oscillators, planetary orbits, rigid-body motion, small vibrations, nonlinear dynamics, chaos, and special relativity. A special feature is the inclusion of many 'e-mail questions', which are intended to facilitate dialogue between the student and instructor. Many worked examples are given, and there are 250 homework exercises to help students gain confidence and proficiency in problem-solving. It is an ideal textbook for undergraduate courses in classical mechanics, and provides a sound foundation for graduate study.

Classical and Analytical Mechanics

Classical and Analytical Mechanics Book
Author : Alex Poznyak
Publisher : Elsevier
Release : 2021-04-08
ISBN : 0323898890
Language : En, Es, Fr & De

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Book Description :

Classical and Analytical Mechanics: Theory, Applied Examples, and Practice provides a bridge between the theory and practice related to mechanical, electrical, and electromechanical systems. It includes rigorous mathematical and physical explanations while maintaining an interdisciplinary engineering focus. Applied problems and exercises in mechanical, mechatronic, aerospace, electrical, and control engineering are included throughout and the book provides detailed techniques for designing models of different robotic, electrical, defense, and aerospace systems. The book starts with multiple chapters covering kinematics before moving onto coverage of dynamics and non-inertial and variable mass systems. Euler’s dynamic equations and dynamic Lagrange equations are covered next with subsequent chapters discussing topics such as equilibrium and stability, oscillation analysis, linear systems, Hamiltonian formalism, and the Hamilton-Jacobi equation. The book concludes with a chapter outlining various electromechanical models that readers can implement and adapt themselves. Bridges theory and practice by providing readers techniques for solving common problems through mechanical, electrical, and electromechanical models alongside the underlying theoretical foundations Describes variable mass, non-inertial systems, dynamic Euler’s equations, gyroscopes, and other related topics Includes a broad offering of practical examples, problems, and exercises across an array of engineering disciplines

Analytical Mechanics

Analytical Mechanics Book
Author : Ioan Merches,Daniel Radu
Publisher : CRC Press
Release : 2014-08-26
ISBN : 148223940X
Language : En, Es, Fr & De

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Book Description :

Giving students a thorough grounding in basic problems and their solutions, Analytical Mechanics: Solutions to Problems in Classical Physics presents a short theoretical description of the principles and methods of analytical mechanics, followed by solved problems. The authors thoroughly discuss solutions to the problems by taking a comprehensive a

Analytical Mechanics

Analytical Mechanics Book
Author : Nivaldo A. Lemos
Publisher : Cambridge University Press
Release : 2018-08-09
ISBN : 1108416586
Language : En, Es, Fr & De

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Book Description :

An introduction to the basic principles and methods of analytical mechanics, with selected examples of advanced topics and areas of ongoing research.

Analytical Mechanics for Relativity and Quantum Mechanics

Analytical Mechanics for Relativity and Quantum Mechanics Book
Author : Oliver Johns
Publisher : Oxford University Press
Release : 2005-07-07
ISBN : 9780198567264
Language : En, Es, Fr & De

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Book Description :

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum mechanics. Comparisons to quantum mechanics appear throughout the text. The extended Hamiltonian theory with time as a coordinate is compared to Dirac's formalism of primary phase space constraints. The chapter on relativisitic mechanics shows how to use covariant Hamiltonian theory to write the Klein-Gordon and Dirac equations. The chapter on Hamilton-Jacobi theory includes a discussion of the closely related Bohm hidden variable model of quantum mechanics. Classical mechanics itself is presented with an emphasis on methods, such as linear vector operators and dyadics, that will familiarize the student with similar techniques in quantum theory. Several of the current fundamental problems in theoretical physics - the development of quantum information technology, and the problem of quantizing the gravitational field, to name two - require a rethinking of the quantum-classical connection. Graduate students preparing for research careers will find a graduate mechanics course based on this book to be an essential bridge between their undergraduate training and advanced study in analytical mechanics, relativity, and quantum mechanics.

Fundamentals of Classical and Analytical Mechanics

Fundamentals of Classical and Analytical Mechanics Book
Author : Krzysztof Lipiński (budowa i eksploatacja maszyn)
Publisher : Unknown
Release : 2021
ISBN : 9788373488311
Language : En, Es, Fr & De

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Book Description :

Download Fundamentals of Classical and Analytical Mechanics book written by Krzysztof Lipiński (budowa i eksploatacja maszyn), available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Analytical Mechanics for Relativity and Quantum Mechanics

Analytical Mechanics for Relativity and Quantum Mechanics Book
Author : Oliver Johns
Publisher : OUP Oxford
Release : 2011-05-19
ISBN : 0191001627
Language : En, Es, Fr & De

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Book Description :

An innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It presents classical mechanics in a way designed to assist the student's transition to quantum theory.

Mechanical Systems Classical Models

Mechanical Systems  Classical Models Book
Author : Petre P. Teodorescu
Publisher : Springer Science & Business Media
Release : 2009-09-30
ISBN : 9048127645
Language : En, Es, Fr & De

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Book Description :

All phenomena in nature are characterized by motion. Mechanics deals with the objective laws of mechanical motion of bodies, the simplest form of motion. In the study of a science of nature, mathematics plays an important rôle. Mechanics is the first science of nature which has been expressed in terms of mathematics, by considering various mathematical models, associated to phenomena of the surrounding nature. Thus, its development was influenced by the use of a strong mathematical tool. As it was already seen in the first two volumes of the present book, its guideline is precisely the mathematical model of mechanics. The classical models which we refer to are in fact models based on the Newtonian model of mechanics, that is on its five principles, i.e.: the inertia, the forces action, the action and reaction, the independence of the forces action and the initial conditions principle, respectively. Other models, e.g., the model of attraction forces between the particles of a discrete mechanical system, are part of the considered Newtonian model. Kepler’s laws brilliantly verify this model in case of velocities much smaller then the light velocity in vacuum.

Analytical Mechanics

Analytical Mechanics Book
Author : A.I. Lurie
Publisher : Springer
Release : 2014-09-12
ISBN : 9783642536502
Language : En, Es, Fr & De

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Book Description :

This is a translation of A.I. Lurie’s classical Russian textbook on analytical mechanics. It offers a consummate exposition of the subject of analytical mechanics through a deep analysis of its most fundamental concepts. The book has served as a desk text for at least two generations of researchers working in those fields where the Soviet Union accomplished the greatest technological breakthrough of the 20th century - a race into space. Those and other related fields continue to be intensively explored since then, and the book clearly demonstrates how the fundamental concepts of mechanics work in the context of up-to-date engineering problems.

Analytical Mechanics

Analytical Mechanics Book
Author : John G Papastavridis
Publisher : World Scientific
Release : 2014-03-06
ISBN : 9814590363
Language : En, Es, Fr & De

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Book Description :

This is a comprehensive, state-of-the-art, treatise on the energetic mechanics of Lagrange and Hamilton, that is, classical analytical dynamics, and its principal applications to constrained systems (contact, rolling, and servoconstraints). It is a book on advanced dynamics from a unified viewpoint, namely, the kinetic principle of virtual work, or principle of Lagrange. As such, it continues, renovates, and expands the grand tradition laid by such mechanics masters as Appell, Maggi, Whittaker, Heun, Hamel, Chetaev, Synge, Pars, Luré, Gantmacher, Neimark, and Fufaev. Many completely solved examples complement the theory, along with many problems (all of the latter with their answers and many of them with hints). Although written at an advanced level, the topics covered in this 1400-page volume (the most extensive ever written on analytical mechanics) are eminently readable and inclusive. It is of interest to engineers, physicists, and mathematicians; advanced undergraduate and graduate students and teachers; researchers and professionals; all will find this encyclopedic work an extraordinary asset; for classroom use or self-study. In this edition, corrections (of the original edition, 2002) have been incorporated. Contents:IntroductionBackground: Basic Concepts and Equations of Particle and Rigid-Body MechanicsKinematics of Constrained SystemsKinetics of Constrained SystemsImpulsive MotionNonlinear Nonholonomic ConstraintsDifferential Variational Principles, and Associated Generalized Equations of Motion of Nielsen, Tsenov, et al.Time-Integral Theorems and Variational PrinciplesIntroduction to Hamiltonian/Canonical Methods: Equations of Hamilton and Routh; Canonical Formalism Readership: Students and researchers in engineering, physics, and applied mathematics. Key Features:No book of this scope (comprehensiveness and state-of-the-art level) has ever been written, in any language, there are no real competitors. This (like the author's other books) is an entirely original work; several of its topics are based on the author's own research, and appear for the first time in book formReadability (“reader friendliness”) in spite of its advanced levelEconomy of thinking: Unified treatment based on Lagrange's kinetic principle of virtual workSuperior and clear notation: both indicial and direct notations for vectors, Cartesian tensors etc.Self-contained exposition: All background mathematics and mechanics are summarized in the handbook like chapter 1Keywords:Analytical Mechanics;Classical Mechanics;Classical Dynamics;Theoretical Mechanics;Advanced Engineering Dynamics;Applied MechanicsReviews: “A monumental treatise … which is going to become a reference book on the subject … It should not be missed by anybody working in the area of analytical dynamics or only wanting to understand major problems of the subject … This landmark reference source … [is] the most comprehensive exposition available of the advanced engineering-oriented dynamics.” Zentralblatt für Math. “This unique treatise should be part of every scientific library and scholarly collection in engineering science.” IEEE Control Systems Magazine “I recommend without hesitation Prof Papastravridis' treatise as a reference source to be acquired by every library of Mathematics, Physics, or Mechanical/Aeronautical/Electrical Engineering department. It is a different book, especially in our Internet era where instant satisfaction is often the primary (sometimes sole) goal of the student or researcher. Putting together 1392 (!!) pages of carefully prepared text and 172 figures (which then become somehow sparse) represents a major effort, to say the least.” Bulletin of the American Mathematical Society “Recipient of the annual competition award, in engineering, of the Association of American Publishers.” The Outstanding Professional and Scholarly Titles of 2002 (March 2003) “Unique in Contents and Perspective … has no Competition in Depth and Breadth.” Dr George Simitses Professor of Engineering Science, Mechanics, and Aerospace Engineering University of Cincinatti and Georgia Institute of Technology, USA “Probably the best of its kind and likely to become standard reference.” Dr Alex Dalgarno FRS, member of US National Academy of Sciences, and “father of molecular astrophysics” and Phillips Professor of Astronomy, Harvard University, and Harvard-Smithsonian Center for Astrophysics, USA “The reviewer shares the author's statement that this book with its almost 1,400 pages is unique among the comparable treatises in the breadth and the depth of the covered material. Regarding technicalities — the students and the young scientists will find a lot of interesting examples and solved up to their very end problems. I recommend you to read this special book in analytical mechanics. It is a useful tool to undergraduate and graduate students, professors and researchers in the area of applied mechanics, engineering science, and mechanical, aerospace, and structural engineering, as well for the physicists and applied mathematicians.” Journal of Geometry and Symmetry in Physics

Mechanical Systems Classical Models

Mechanical Systems  Classical Models Book
Author : Anonim
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Mechanical Systems Classical Models book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Mechanical Systems Classical Models

Mechanical Systems  Classical Models Book
Author : Petre P. Teodorescu
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Mechanical Systems Classical Models book written by Petre P. Teodorescu, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Analytical Mechanics

Analytical Mechanics Book
Author : Antonio Fasano,Stefano Marmi
Publisher : OUP Oxford
Release : 2006-04-06
ISBN : 9780191513596
Language : En, Es, Fr & De

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Book Description :

Analytical Mechanics is the investigation of motion with the rigorous tools of mathematics, with remarkable applications to many branches of physics (Astronomy, Statistical and Quantum Mechanics, etc.). Rooted in the works of Lagrange, Euler, and Poincaré, it is a classical subject with fascinating developments and still rich with open problems. It addresses such fundamental questions as: Is the solar system stable? Is there a unifying "economy" principle in mechanics? How can a point mass be described as a "wave"? This book was written to fill a gap between elementary expositions and more advanced (and clearly more stimulating) material. It takes the challenge to explain the most relevant ideas and to show the most important applications using plain language and "simple" mathematics, often through an original approach. Basic calculus is enough for the reader to proceed through the book and when more is required, the new mathematical concepts are illustrated, again in plain language. The book is conceived in such a way that some difficult chapters can be bypassed, whilst still grasping the main ideas. However, anybody wishing to go deeper in some directions will find at least the flavour of recent developments and many bibliographical references. Theory is always accompanied by examples. Many problems are suggested and some are completely worked out at the end of each chapter. The book may effectively be used (and it is in several Italian Universities) for undergraduate as well as for PhD courses in Physics and Mathematics at various levels.

Introduction to Classical Mechanics

Introduction to Classical Mechanics Book
Author : Roy, Nikhil Ranjan
Publisher : Vikas Publishing House
Release : 2022-01-20
ISBN : 932599402X
Language : En, Es, Fr & De

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Book Description :

The book deals with the mechanics of particles and rigid bodies. It is written for the undergraduate students of physics and meets the syllabus requirements of most Indian universities. It also covers the entire syllabus on classical/analytical mechanics for various national and state level examinations like NET, GATE and SLET. Some of the topics in the book are included in the curricula of applied mathematics in several institutions as well.KEY FEATURES• Main emphasis is on the evolution of the subject, the underlying ideas, the concepts, the laws and the mathematical methods• Written in the style of classroom teaching so that the students may benefit from it by way of self-study• Step-by-step derivation of concepts, with each step clearly numbered• Concepts explained with the help of relevant examples to aid understanding

Lagrangian and Hamiltonian Analytical Mechanics Forty Exercises Resolved and Explained

Lagrangian and Hamiltonian Analytical Mechanics  Forty Exercises Resolved and Explained Book
Author : Vladimir Pletser
Publisher : Springer
Release : 2018-11-23
ISBN : 9811330263
Language : En, Es, Fr & De

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Book Description :

This textbook introduces readers to the detailed and methodical resolution of classical and more recent problems in analytical mechanics. This valuable learning tool includes worked examples and 40 exercises with step-by-step solutions, carefully chosen for their importance in classical, celestial and quantum mechanics. The collection comprises six chapters, offering essential exercises on: (1) Lagrange Equations; (2) Hamilton Equations; (3) the First Integral and Variational Principle; (4) Canonical Transformations; (5) Hamilton – Jacobi Equations; and (6) Phase Integral and Angular Frequencies Each chapter begins with a brief theoretical review before presenting the clearly solved exercises. The last two chapters are of particular interest, because of the importance and flexibility of the Hamilton-Jacobi method in solving many mechanical problems in classical mechanics, as well as quantum and celestial mechanics. Above all, the book provides students and teachers alike with detailed, point-by-point and step-by-step solutions of exercises in Lagrangian and Hamiltonian mechanics, which are central to most problems in classical physics, astronomy, celestial mechanics and quantum physics.

Analytical Mechanics

Analytical Mechanics Book
Author : Carl S. Helrich
Publisher : Springer
Release : 2016-10-01
ISBN : 3319444913
Language : En, Es, Fr & De

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Book Description :

This advanced undergraduate textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations, with constraints incorporated through Lagrange multipliers. Hamilton's Principle and the canonical equations remain the basis of the remainder of the text. Topics considered for applications include small oscillations, motion in electric and magnetic fields, and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally the text has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance. The text is enriched with an outline of the history of mechanics, which particularly outlines the importance of the work of Euler, Lagrange, Hamilton and Jacobi. Numerous exercises with solutions support the exceptionally clear and concise treatment of Analytical Mechanics.

Analytical Mechanics

Analytical Mechanics Book
Author : Grant R. Fowles,George L. Cassiday
Publisher : Brooks/Cole Publishing Company
Release : 2005
ISBN : 9780534494926
Language : En, Es, Fr & De

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Book Description :

Master introductory mechanics with ANALYTICAL MECHANICS! Direct and practical, this physics text is designed to help you grasp the challenging concepts of physics. Specific cases are included to help you master theoretical material. Numerous worked examples found throughout increase your problem-solving skills and prepare you to succeed on tests.

Introduction to Analytical Mechanics

Introduction to Analytical Mechanics Book
Author : K. a. i. l. w. Gamalath
Publisher : Alpha Science International Limited
Release : 2011
ISBN : 9781842656686
Language : En, Es, Fr & De

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Book Description :

INTRODUCTION TO ANALYTICAL MECHANICS is an attempt to introduce the modern treatment of classical mechanics so that transition to many fields in physics can be made with the least difficulty. This book deal with the formulation of Newtonian mechanics, Lagrangian dynamics, conservation laws relating to symmetries, Hamiltonian dynamics Hamilton's principle, Poisson brackets, canonical transformations which are invaluable in formulating the quantum mechanics and Hamilton-Jacobi equation which provides the transition to wave mechanics.

Exploring Classical Mechanics

Exploring Classical Mechanics Book
Author : Full Professor and Chair of Theoretical Physics G L Kotkin,G. L. Kotkin,Full Professor and Chair of Theoretical Physics V G Serbo,V. G. Serbo
Publisher : Oxford University Press, USA
Release : 2020-08-10
ISBN : 0198853785
Language : En, Es, Fr & De

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Book Description :

This new edition of a popular textbook offers an original collection of problems in analytical mechanics. Analytical mechanics is the first chapter in the study and understanding of theoretical physics. Its methods and ideas are crucially important, as they form the basis of all other branches of theoretical physics, including quantum mechanics, statistical physics, and field theory. Such concepts as the Lagrangian and Hamiltonian formalisms, normal oscillations, adiabatic invariants, Liouville theorem, and canonical transformations lay the foundation, without which any further in-depth study of theoretical physics is impossible. Wherever possible, the authors draw analogies and comparisons with similar processes in electrodynamics, quantum mechanics, or statistical mechanics while presenting the solutions to the problems. The book is based on the authors' many years of experience delivering lectures and seminars at the Department of Physics at Novosibirsk State University -- totalling an impressive 110+ years of combined teaching experience. Most of the problems are original, and will be useful not only for those studying mechanics, but also for those who teach it. The content of the book corresponds to and roughly follows the mechanics course in the well-known textbooks by Landau and Lifshitz, Goldstein, or ter Haar. The Collection... starts with the Newtonian equations, motion in a central field, and scattering. Then the text proceeds to the established, traditional sections of analytical mechanics as part of the course on theoretical physics: the Lagrangian equations, the Noether theorem, linear and nonlinear oscillations, Hamilton formalism, and motion of a solid body. As a rule, the solution of a problem is not complete by just obtaining the required formulae. It's necessary to analyse the result. This can be an interesting process of discovery for the student and is by no means a "mechanical'' part of the solution. It is also very useful to investigate what happens if the conditions of the problem are varied. With this in mind, the authors offer suggestions of further problems at the end of several solutions. First published in 1969 in Russian, this text has become widely used in classrooms around the world. It has been translated into several languages, and has seen multiple editions in various languages.

Analytical Mechanics

Analytical Mechanics Book
Author : Louis Hand
Publisher : Unknown
Release : 1998
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Analytical Mechanics, first published in 1999, provides a detailed introduction to the key analytical techniques of classical mechanics, one of the cornerstones of physics. It deals with all the important subjects encountered in an undergraduate course and prepares the reader thoroughly for further study at graduate level. The authors set out the fundamentals of Lagrangian and Hamiltonian mechanics early on in the book and go on to cover such topics as linear oscillators, planetary orbits, rigid-body motion, small vibrations, nonlinear dynamics, chaos, and special relativity. A special feature is the inclusion of many 'e-mail questions', which are intended to facilitate dialogue between the student and instructor. Many worked examples are given, and there are 250 homework exercises to help students gain confidence and proficiency in problem-solving. It is an ideal textbook for undergraduate courses in classical mechanics, and provides a sound foundation for graduate study.