Fundamental Principles Of Classical Mechanics A Geometrical Perspective

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Fundamental Principles Of Classical Mechanics A Geometrical Perspective

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Author : Kai S Lam
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-07-07

Fundamental Principles Of Classical Mechanics A Geometrical Perspective written by Kai S Lam 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 2014-07-07 with Science categories.

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).

Fundamental Principles Of Classical Mechanics

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Author : Kai Shue Lam
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2014

Fundamental Principles Of Classical Mechanics written by Kai Shue Lam and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Science categories.

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).

Essential Classical Mechanics

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Author : Choonkyu Lee
language : en
Publisher: World Scientific Publishing Company
Release Date : 2018-04-17

Essential Classical Mechanics written by Choonkyu Lee 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 2018-04-17 with Science categories.

'The authors deliver a highly readable text which should assure a continued supply of practitioners of classical mechanics and its applications.'Contemporary PhysicsThis is a book on intermediate classical mechanics. In this book, classical mechanics is presented as a useful tool to analyze the physical universe and also as the base on which the whole pyramid of modern physics has been erected. Various mechanical concepts are developed in a highly logical manner, with relatively thorough treatments on mathematical procedures and many physically interesting applications. Connections to more modern theoretical developments (including statistical physics, relativity, and quantum mechanics) are emphasized.

Essential Classical Mechanics Problems And Solutions

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Author : Choonkyu Lee
language : en
Publisher: World Scientific
Release Date : 2018-07-10

Essential Classical Mechanics Problems And Solutions written by Choonkyu Lee and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-10 with Science categories.

'The authors of this book offer a very strong reason for the study of classical mechanics describing it 'as the base on which the whole pyramid of modern physics has been erected' … In order that students can gauge their understanding of the various topics, many exercises are introduced. Some of those should be straightforward whilst others are quite challenging … The authors are to be thanked for delivering a highly readable text which should assure a continued supply of practitioners of classical mechanics and its applications.'Contemporary PhysicsProblem solving in physics is not simply a test of understanding, but an integral part of learning. This book contains complete step-by-step solutions for all exercise problems in Essential Classical Mechanics, with succinct chapter-by-chapter summaries of key concepts and formulas. The degree of difficulty with problems varies from quite simple to very challenging; but none too easy, as all problems in physics demand some subtlety of intuition. The emphasis of the book is not so much in acquainting students with various problem-solving techniques as in suggesting ways of thinking. For undergraduate and graduate students, as well as those involved in teaching classical mechanics, this book can be used as a supplementary text or as an independent study aid.

Analytical Mechanics

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Author : Nivaldo A. Lemos
language : en
Publisher: Cambridge University Press
Release Date : 2018-08-09

Analytical Mechanics written by Nivaldo A. Lemos 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 2018-08-09 with Science categories.

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

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.

Classical Dynamics A Modern Perspective

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Author : E C George Sudarshan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-10-08

Classical Dynamics A Modern Perspective written by E C George Sudarshan 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 2015-10-08 with Science categories.

Classical dynamics is traditionally treated as an early stage in the development of physics, a stage that has long been superseded by more ambitious theories. Here, in this book, classical dynamics is treated as a subject on its own as well as a research frontier. Incorporating insights gained over the past several decades, the essential principles of classical dynamics are presented, while demonstrating that a number of key results originally considered only in the context of quantum theory and particle physics, have their foundations in classical dynamics.Graduate students in physics and practicing physicists will welcome the present approach to classical dynamics that encompasses systems of particles, free and interacting fields, and coupled systems. Lie groups and Lie algebras are incorporated at a basic level and are used in describing space-time symmetry groups. There is an extensive discussion on constrained systems, Dirac brackets and their geometrical interpretation. The Lie-algebraic description of dynamical systems is discussed in detail, and Poisson brackets are developed as a realization of Lie brackets. Other topics include treatments of classical spin, elementary relativistic systems in the classical context, irreducible realizations of the Galileo and Poincaré groups, and hydrodynamics as a Galilean field theory. Students will also find that this approach that deals with problems of manifest covariance, the no-interaction theorem in Hamiltonian mechanics and the structure of action-at-a-distance theories provides all the essential preparatory groundwork for a passage to quantum field theory.This reprinting of the original text published in 1974 is a testimony to the vitality of the contents that has remained relevant over nearly half a century.

Classical Mechanics

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Author : Jan Awrejcewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-26

Classical Mechanics written by Jan Awrejcewicz 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 2012-07-26 with Science categories.

This is the first volume of three, devoted to Mechanics. This book contains classical mechanics problems including kinematics and statics. It is recommended as a supplementary textbook for undergraduate and graduate students from mechanical and civil engineering, as well as for physical scientists and engineers. It contains a basic introduction to classical mechanics, including fundamental principles, statics, and the geometry of masses, as well as thorough discussion on kinematics.

Fundamentals Of Tensor Calculus For Engineers With A Primer On Smooth Manifolds

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Author : Uwe Mühlich
language : en
Publisher: Springer
Release Date : 2017-04-18

Fundamentals Of Tensor Calculus For Engineers With A Primer On Smooth Manifolds written by Uwe Mühlich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-18 with Science categories.

This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.

Geometric Mechanics Dynamics And Symmetry

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Author : Darryl D. Holm
language : en
Publisher: Imperial College Press
Release Date : 2008-01-01

Geometric Mechanics Dynamics And Symmetry written by Darryl D. Holm and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.

Advanced undergraduate and graduate students in mathematics, physics and engineering.