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Mathematical Methods Of Analytical Mechanics

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Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics Book
Author : V.I. Arnol'd
Publisher : Springer Science & Business Media
Release : 2013-04-09
ISBN : 1475720637
Language : En, Es, Fr & De

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Book Description :

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.

Mathematical Methods of Analytical Mechanics

Mathematical Methods of Analytical Mechanics Book
Author : Henri Gouin
Publisher : Elsevier
Release : 2020-11-27
ISBN : 0128229861
Language : En, Es, Fr & De

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Book Description :

Mathematical Methods of Analytical Mechanics uses tensor geometry and geometry of variation calculation, includes the properties associated with Noether's theorem, and highlights methods of integration, including Jacobi's method, which is deduced. In addition, the book covers the Maupertuis principle that looks at the conservation of energy of material systems and how it leads to quantum mechanics. Finally, the book deduces the various spaces underlying the analytical mechanics which lead to the Poisson algebra and the symplectic geometry. Helps readers understand calculations surrounding the geometry of the tensor and the geometry of the calculation of the variation Presents principles that correspond to the energy conservation of material systems Defines the invariance properties associated with Noether's theorem Discusses phase space and Liouville's theorem Identifies small movements and different types of stabilities

Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics Book
Author : V. I. Arnold
Publisher : Springer Science & Business Media
Release : 2013-11-11
ISBN : 1475716931
Language : En, Es, Fr & De

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Book Description :

Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians.

Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics Book
Author : V.I. Arnol'd
Publisher : Springer Science & Business Media
Release : 1997-09-05
ISBN : 9780387968902
Language : En, Es, Fr & De

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Book Description :

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.

Methods of Differential Geometry in Analytical Mechanics

Methods of Differential Geometry in Analytical Mechanics Book
Author : M. de León,P.R. Rodrigues
Publisher : Elsevier
Release : 2011-08-18
ISBN : 9780080872698
Language : En, Es, Fr & De

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Book Description :

The differential geometric formulation of analytical mechanics not only offers a new insight into Mechanics, but also provides a more rigorous formulation of its physical content from a mathematical viewpoint. Topics covered in this volume include differential forms, the differential geometry of tangent and cotangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories. The book may be considered as a self-contained text and only presupposes that readers are acquainted with linear and multilinear algebra as well as advanced calculus.

Mathematical Aspects of Classical and Celestial Mechanics

Mathematical Aspects of Classical and Celestial Mechanics Book
Author : Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt
Publisher : Springer Science & Business Media
Release : 2007-07-05
ISBN : 3540489266
Language : En, Es, Fr & De

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Book Description :

The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

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 : 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.

Analytical Mechanics

Analytical Mechanics Book
Author : Joseph S. Torok
Publisher : John Wiley & Sons
Release : 1999-11-04
ISBN : 9780471332077
Language : En, Es, Fr & De

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Book Description :

A stimulating, modern approach to analytical mechanics Analytical Mechanics with an Introduction to Dynamical Systems offers a much-needed, up-to-date treatment of analytical dynamics to meet the needs of today's students and professionals. This outstanding resource offers clear and thorough coverage of mechanics and dynamical systems, with an approach that offers a balance between physical fundamentals and mathematical concepts. Exceptionally well written and abundantly illustrated, the book contains over 550 new problems-more than in any other book on the subject-along with user-friendly computational models using MATLAB. Featured topics include: * An overview of fundamental dynamics, both two- and three-dimensional * An examination of variational approaches, including Lagrangian theory * A complete discussion of the dynamics of rotating bodies * Coverage of the three-dimensional dynamics of rigid bodies * A detailed treatment of Hamiltonian systems and stability theory Ideal for advanced undergraduate and graduate students in mechanical engineering, physics, or applied mathematics, this distinguished text is also an excellent self-study or reference text for the practicing engineer or scientist.

Analytical Mechanics

Analytical Mechanics Book
Author : A.I. Lurie
Publisher : Springer Science & Business Media
Release : 2002-03-26
ISBN : 9783540429821
Language : En, Es, Fr & De

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Book Description :

This is a translation of A.I. Lurie classical Russian textbook on analytical mechanics. Part of it is based on courses formerly held by the author. 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 XX 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. This book will help researchers and graduate students to acquire a deeper insight into analytical mechanics.

Modern Methods of Analytical Mechanics and Their Applications

Modern Methods of Analytical Mechanics and Their Applications Book
Author : Valentin V. Rumyantsev,Alexander V. Karapetyan
Publisher : Springer
Release : 1998-10-27
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The volume aims at giving a comprehensive and up-to-date view of modern methods of analytical mechanics (general equations, invariant objects, stability and bifurcations) and their applications (rigid body dynamics, celestial mechanics, multibody systems etc.). The course is at an advanced level. It is designed for postgraduate students, research engineers and academics that are familiar with basic concepts of analytical dynamics and stability theory. Although the course deals with mechanical problems, most of the concepts and methods involved are equally applicated to general dynamical systems.

Mathematical Methods In Classical And Quantum Physics

Mathematical Methods In Classical And Quantum Physics Book
Author : Tulsi Dass,S.K. Sharma
Publisher : Universities Press
Release : 1998
ISBN : 9788173710896
Language : En, Es, Fr & De

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Book Description :

This book is intended to provide an adequate background for various theortical physics courses, especially those in classical mechanics, electrodynamics, quatum mechanics and statistical physics. Each topic is dealt with in a generally self-contained manner and the text is interspersed with a number of solved examples ad a large number of exercise problems.

Introduction to Classical Mechanics

Introduction to Classical Mechanics Book
Author : Roy, Nikhil Ranjan
Publisher : Vikas Publishing House
Release : 2021-05-13
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

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.

Fundamental Principles of Classical Mechanics

Fundamental Principles of Classical Mechanics Book
Author : Kai S Lam
Publisher : World Scientific Publishing Company
Release : 2014-07-07
ISBN : 9814551503
Language : En, Es, Fr & De

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Book Description :

This book is written with the belief that classical mechanics, as a theoretical discipline, possesses an inherent beauty, depth, and richness that far transcends its immediate applications in mechanical systems. These properties are manifested, by and large, through the coherence and elegance of the mathematical structure underlying the discipline, and are eminently worthy of being communicated to physics students at the earliest stage possible. This volume is therefore addressed mainly to advanced undergraduate and beginning graduate physics students who are interested in the application of modern mathematical methods in classical mechanics, in particular, those derived from the fields of topology and differential geometry, and also to the occasional mathematics student who is interested in important physics applications of these areas of mathematics. Its main purpose is to offer an introductory and broad glimpse of the majestic edifice of the mathematical theory of classical dynamics, not only in the time-honored analytical tradition of Newton, Laplace, Lagrange, Hamilton, Jacobi, and Whittaker, but also the more topological/geometrical one established by Poincare, and enriched by Birkhoff, Lyapunov, Smale, Siegel, Kolmogorov, Arnold, and Moser (as well as many others).

Theoretical Physics 7

Theoretical Physics 7 Book
Author : Wolfgang Nolting
Publisher : Springer
Release : 2017-09-27
ISBN : 3319633244
Language : En, Es, Fr & De

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Book Description :

This textbook offers a clear and comprehensive introduction to methods and applications in quantum mechanics, one of the core components of undergraduate physics courses. It follows on naturally from the previous volumes in this series, thus developing the understanding of quantized states further on. The first part of the book introduces the quantum theory of angular momentum and approximation methods. More complex themes are covered in the second part of the book, which describes multiple particle systems and scattering theory. Ideally suited to undergraduate students with some grounding in the basics of quantum 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.

Mathematical Methods for Mechanics

Mathematical Methods for Mechanics Book
Author : Eckart W. Gekeler
Publisher : Springer Science & Business Media
Release : 2008-09-26
ISBN : 3540692797
Language : En, Es, Fr & De

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Book Description :

Mathematics is undoubtedly the key to state-of-the-art high technology. It is aninternationaltechnicallanguageandprovestobeaneternallyyoungscience to those who have learned its ways. Long an indispensable part of research thanks to modeling and simulation, mathematics is enjoying particular vit- ity now more than ever. Nevertheless, this stormy development is resulting in increasingly high requirements for students in technical disciplines, while general interest in mathematics continues to wane at the same time. This book and its appendices on the Internet seek to deal with this issue, helping students master the di?cult transition from the receptive to the productive phase of their education. The author has repeatedly held a three-semester introductory course - titled Higher Mathematics at the University of Stuttgart and used a series of “handouts” to show further aspects, make the course contents more motiv- ing, and connect with the mechanics lectures taking place at the same time. One part of the book has more or less evolved from this on its own. True to the original objective, this part treats a variety of separate topics of varying degrees of di?culty; nevertheless, all these topics are oriented to mechanics. Anotherpartofthisbookseekstoo?eraselectionofunderstandablereal- ticmodelsthatcanbeimplementeddirectlyfromthemultitudeofmathema- calresources.TheauthordoesnotattempttohidehispreferenceofNumerical Mathematics and thus places importance on careful theoretical preparation.

Mathematical Methods for Physical and Analytical Chemistry

Mathematical Methods for Physical and Analytical Chemistry Book
Author : David Z. Goodson
Publisher : John Wiley & Sons
Release : 2011-11-14
ISBN : 1118135172
Language : En, Es, Fr & De

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Book Description :

Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton’s method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical knowledge they need to understand the analytical and physical chemistry professional literature.

Classical Mechanics

Classical Mechanics Book
Author : Dieter Strauch
Publisher : Springer Science & Business Media
Release : 2009-06-07
ISBN : 3540736166
Language : En, Es, Fr & De

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Book Description :

This upper-level undergraduate and beginning graduate textbook primarily covers the theory and application of Newtonian and Lagrangian, but also of Hamiltonian mechanics. In addition, included are elements of continuum mechanics and the accompanying classical field theory, wherein four-vector notation is introduced without explicit reference to special relativity. The author's writing style attempts to ease students through the primary and secondary results, thus building a solid foundation for understanding applications. Numerous examples illustrate the material and often present alternative approaches to the final results.

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.