Mathematical Methods Of Classical Mechanics
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Mathematical Methods Of Classical Mechanics
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Author : V. I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Mathematical Methods Of Classical Mechanics written by V. I. Arnold 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 2013-11-11 with Mathematics categories.
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
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Author : V.I. Arnol'd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Mathematical Methods Of Classical Mechanics written by V.I. Arnol'd 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 2013-04-09 with Mathematics categories.
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Mathematical Methods Of Classical Mechanics
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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher:
Release Date : 1997
Mathematical Methods Of Classical Mechanics written by Vladimir Igorevich Arnolʹd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mechanics, Analytic categories.
Mathematical Methods Of Classical Mechanics
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Author : Vladimir Igor'evič Arnol'd
language : en
Publisher:
Release Date : 1978
Mathematical Methods Of Classical Mechanics written by Vladimir Igor'evič Arnol'd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
Mathematical Methods Of Classical Mechanics
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Author : V. I. Arnol'd
language : en
Publisher:
Release Date : 2014-01-15
Mathematical Methods Of Classical Mechanics written by V. I. Arnol'd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Mathematical Methods Of Classical Physics
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Author : Vicente Cortés
language : en
Publisher: Springer
Release Date : 2017-04-26
Mathematical Methods Of Classical Physics written by Vicente Cortés and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-26 with Science categories.
This short primer, geared towards students with a strong interest in mathematically rigorous approaches, introduces the essentials of classical physics, briefly points out its place in the history of physics and its relation to modern physics, and explains what benefits can be gained from a mathematical perspective. As a starting point, Newtonian mechanics is introduced and its limitations are discussed. This leads to and motivates the study of different formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, which are the subjects of later chapters. In the second part, a chapter on classical field theories introduces more advanced material. Numerous exercises are collected in the appendix.
Mathematical Methods In Classical And Quantum Physics
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Author : Tulsi Dass
language : en
Publisher: Universities Press
Release Date : 1998
Mathematical Methods In Classical And Quantum Physics written by Tulsi Dass and has been published by Universities Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematical physics categories.
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.
Mathematical Methods For Mechanics
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Author : Eckart W. Gekeler
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-26
Mathematical Methods For Mechanics written by Eckart W. Gekeler 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 2008-09-26 with Technology & Engineering categories.
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.
Classical Mechanics
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Author : Joseph L. McCauley
language : en
Publisher: Cambridge University Press
Release Date : 1997-05-08
Classical Mechanics written by Joseph L. McCauley 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 1997-05-08 with Science categories.
This advanced text is the first book to describe the subject of classical mechanics in the context of the language and methods of modern nonlinear dynamics. The organizing principle of the text is integrability vs. nonintegrability.
Classical Mechanics
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Author : Alexei Deriglazov
language : en
Publisher: Springer
Release Date : 2016-10-08
Classical Mechanics written by Alexei Deriglazov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-08 with Science categories.
The revised edition of this advanced textbook provides the reader with a solid grounding in the formalism of classical mechanics, underlying a number of powerful mathematical methods that are widely used in modern theoretical and mathematical physics. It reviews the fundamentals of Lagrangian and Hamiltonian mechanics, and goes on to cover 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. New material for the revised edition includes additional sections on the Euler-Lagrange equation, the Cartan two-form in Lagrangian theory, and Newtonian equations of motion in context of general relativity. Also new for this edition is the inclusion of problem sets and solutions to aid in the understanding of the material presented. The mathematical constructions involved are explicitly described and explained, so the book is a good starting point for the student new to this field. Where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for more advanced 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.