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Classical and Analytical Mechanics

Classical and Analytical Mechanics Book
Author : Alexander S. Poznyak
Publisher : Elsevier
Release : 2021-05-03
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 : 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.

Analytical Mechanics

Analytical Mechanics Book
Author : Ioan Merches,Daniel Radu
Publisher : CRC Press
Release : 2014-08-26
ISBN : 1482239396
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 approach to explore the methods of investigation. They carefully perform the calculations step by step, graphically displaying some solutions via Mathematica® 4.0. This collection of solved problems gives students experience in applying theory (Lagrangian and Hamiltonian formalisms for discrete and continuous systems, Hamilton-Jacobi method, variational calculus, theory of stability, and more) to problems in classical physics. The authors develop some theoretical subjects, so that students can follow solutions to the problems without appealing to other reference sources. This has been done for both discrete and continuous physical systems or, in analytical terms, systems with finite and infinite degrees of freedom. The authors also highlight the basics of vector algebra and vector analysis, in Appendix B. They thoroughly develop and discuss notions like gradient, divergence, curl, and tensor, together with their physical applications. There are many excellent textbooks dedicated to applied analytical mechanics for both students and their instructors, but this one takes an unusual approach, with a thorough analysis of solutions to the problems and an appropriate choice of applications in various branches of physics. It lays out the similarities and differences between various analytical approaches, and their specific efficiency.

A Primer of Analytical Mechanics

A Primer of Analytical Mechanics Book
Author : Franco Strocchi
Publisher : Springer
Release : 2018-03-09
ISBN : 3319737619
Language : En, Es, Fr & De

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Book Description :

This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hamiltonian canonical algebra and its effectiveness in simplifying the control of the dynamical problem (e.g. the constant of motions identified by the Poisson brackets with the Hamiltonian, the relation between symmetries and conservations laws, the use of canonical transformations to reduce the Hamiltonian to a simpler form etc.). The book also addresses a number of points usually not included in textbook presentations of Analytical Mechanics, such as 1) the characterization of the cases in which the Hamiltonian differs from the energy, 2) the characterization of the non-uniqueness of the Lagrangian and of the Hamiltonian and its relation to a “gauge” transformation, 3) the Hamiltonian formulation of the Noether theorem, with the possibility that the constant of motion corresponding to a continuous symmetry of the dynamics is not the canonical generator of the symmetry transformation but also involves the generator of a gauge transformation. In turn, the book’s closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum Mechanics, the differences between the two theories being reducible to the value of the central variable of that algebra.

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

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.

Theoretical Physics 2

Theoretical Physics 2 Book
Author : Wolfgang Nolting
Publisher : Springer
Release : 2016-06-28
ISBN : 3319401297
Language : En, Es, Fr & De

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Book Description :

This textbook offers a clear and comprehensive introduction to analytical mechanics, one of the core components of undergraduate physics courses. The book starts with a thorough introduction into Lagrangian mechanics, detailing the d’Alembert principle, Hamilton’s principle and conservation laws. It continues with an in-depth explanation of Hamiltonian mechanics, illustrated by canonical and Legendre transformation, the generalization to quantum mechanics through Poisson brackets and all relevant variational principles. Finally, the Hamilton-Jacobi theory and the transition to wave mechanics are presented in detail. Ideally suited to undergraduate students with some grounding in classical mechanics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successful German editions, the eight volumes of this series cover the complete core curriculum of theoretical physics at undergraduate level. Each volume is self-contained and provides all the material necessary for the individual course topic. Numerous problems with detailed solutions support a deeper understanding. Wolfgang Nolting is famous for his refined didactical style and has been referred to as the "German Feynman" in reviews.

Mechanical Systems Classical Models

Mechanical Systems  Classical Models Book
Author : Petre P. Teodorescu
Publisher : Springer Science & Business Media
Release : 2009-09-30
ISBN : 9789048127641
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.

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 of Space Systems

Analytical Mechanics of Space Systems Book
Author : Hanspeter Schaub,John L. Junkins
Publisher : AIAA
Release : 2003
ISBN : 9781600860270
Language : En, Es, Fr & De

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Book Description :

Download Analytical Mechanics of Space Systems book written by Hanspeter Schaub,John L. Junkins, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Classical Mechanics

Classical Mechanics Book
Author : R. Douglas Gregory
Publisher : Cambridge University Press
Release : 2006-04-13
ISBN : 1139450042
Language : En, Es, Fr & De

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Book Description :

Gregory's Classical Mechanics is a major new textbook for undergraduates in mathematics and physics. It is a thorough, self-contained and highly readable account of a subject many students find difficult. The author's clear and systematic style promotes a good understanding of the subject: each concept is motivated and illustrated by worked examples, while problem sets provide plenty of practice for understanding and technique. Computer assisted problems, some suitable for projects, are also included. The book is structured to make learning the subject easy; there is a natural progression from core topics to more advanced ones and hard topics are treated with particular care. A theme of the book is the importance of conservation principles. These appear first in vectorial mechanics where they are proved and applied to problem solving. They reappear in analytical mechanics, where they are shown to be related to symmetries of the Lagrangian, culminating in Noether's theorem.

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 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.

Analytical Mechanics

Analytical Mechanics Book
Author : Grant R. Fowles
Publisher : Saunders College Publishing
Release : 1986
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Analytical Mechanics book written by Grant R. Fowles, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Introduction to Classical Mechanics

Introduction to Classical Mechanics Book
Author : Roy, Nikhil Ranjan
Publisher : Vikas Publishing House
Release : 2021-04-16
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

Solved Problems in Classical Mechanics

Solved Problems in Classical Mechanics Book
Author : O.L. de Lange,J. Pierrus
Publisher : Oxford University Press
Release : 2010-05-06
ISBN : 0199582521
Language : En, Es, Fr & De

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Book Description :

simulated motion on a computer screen, and to study the effects of changing parameters. --

Mechanical Systems Classical Models

Mechanical Systems  Classical Models Book
Author : P. 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 P. P. Teodorescu, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Classical Mechanics

Classical Mechanics Book
Author : Herbert Charles Corben,Philip Stehle
Publisher : Courier Corporation
Release : 1994-01-01
ISBN : 9780486680637
Language : En, Es, Fr & De

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Book Description :

Applications not usually taught in physics courses include theory of space-charge limited currents, atmospheric drag, motion of meteoritic dust, variational principles in rocket motion, transfer functions, much more. 1960 edition."

Analytical Mechanics

Analytical Mechanics Book
Author : John G. Papastavridis
Publisher : World Scientific Publishing Company Incorporated
Release : 2014
ISBN : 9789814338714
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.

A Student s Guide to Analytical Mechanics

A Student s Guide to Analytical Mechanics Book
Author : John L. Bohn
Publisher : Cambridge University Press
Release : 2018-09-30
ISBN : 1107145767
Language : En, Es, Fr & De

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Book Description :

An accessible guide to analytical mechanics, using intuitive examples to illustrate the underlying mathematics, helping students formulate, solve and interpret problems in mechanics.