Fundamental Principles Of Classical Mechanics: A Geometrical Perspective

Fundamental Principles Of Classical Mechanics: A Geometrical Perspective
Author: Kai S Lam
Publisher: World Scientific Publishing Company
Total Pages: 591
Release: 2014-07-07
Genre: Science
ISBN: 9814551503

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

Fundamental Principles of Classical Mechanics
Author: Kai Shue Lam
Publisher: World Scientific Publishing Company Incorporated
Total Pages: 574
Release: 2014
Genre: Science
ISBN: 9789814551489

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).

Geometric Mechanics

Geometric Mechanics
Author: Richard Talman
Publisher: John Wiley & Sons
Total Pages: 582
Release: 2008-07-11
Genre: Science
ISBN: 3527617817

Mechanics for the nonmathematician-a modern approach For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest . . . APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.

Classical Mechanics

Classical Mechanics
Author: Jan Awrejcewicz
Publisher: Springer Science & Business Media
Total Pages: 453
Release: 2012-07-26
Genre: Science
ISBN: 1461437911

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.

Mathematical Aspects of Classical and Celestial Mechanics

Mathematical Aspects of Classical and Celestial Mechanics
Author: Vladimir I. Arnold
Publisher: Springer Science & Business Media
Total Pages: 505
Release: 2007-07-05
Genre: Mathematics
ISBN: 3540489266

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.

Classical Mechanics

Classical Mechanics
Author: Emmanuele DiBenedetto
Publisher: Springer Science & Business Media
Total Pages: 364
Release: 2010-10-17
Genre: Mathematics
ISBN: 0817646485

* Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries

Essential Classical Mechanics

Essential Classical Mechanics
Author: Choonkyu Lee
Publisher: World Scientific Publishing Company
Total Pages: 717
Release: 2018-04-17
Genre: Science
ISBN: 9813234660

'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.

Classical Dynamics: A Modern Perspective

Classical Dynamics: A Modern Perspective
Author: E C George Sudarshan
Publisher: World Scientific Publishing Company
Total Pages: 612
Release: 2015-10-08
Genre: Science
ISBN: 9814713899

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.

Essential Classical Mechanics: Problems And Solutions

Essential Classical Mechanics: Problems And Solutions
Author: Choonkyu Lee
Publisher: World Scientific
Total Pages: 506
Release: 2018-07-10
Genre: Science
ISBN: 9813270071

'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.

Geometric Mechanics

Geometric Mechanics
Author: Richard Talman
Publisher: Wiley-VCH
Total Pages: 0
Release: 2007-07-10
Genre: Science
ISBN: 9783527406838

For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for non-mathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, the author treats Lagrangian, Hamiltonian, and Newtonian mechanics separately -- exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. This second, fully revised edition has been expanded to include new chapters on electromagnetic theory, general relativity, and string theory. 'Geometric Mechanics' features illustrative examples and assumes only basic knowledge of Lagrangian mechanics.