Methods Of Differential Geometry In Analytical Mechanics
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Methods Of Differential Geometry In Analytical Mechanics
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Author : M. de León
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Methods Of Differential Geometry In Analytical Mechanics written by M. de León and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
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.
Methods Of Differential Geometry In Analytical Mechanics
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Author : Manuel de León
language : en
Publisher: North Holland
Release Date : 1989
Methods Of Differential Geometry In Analytical Mechanics written by Manuel de León and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Geometry, Differential categories.
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.
Geometric Mechanics On Riemannian Manifolds
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Author : Ovidiu Calin
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Geometric Mechanics On Riemannian Manifolds written by Ovidiu Calin 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 2006-03-30 with Mathematics categories.
* A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics
Lectures On Differential Geometry
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Author : Iskander Asanovich Taĭmanov
language : en
Publisher: European Mathematical Society
Release Date : 2008
Lectures On Differential Geometry written by Iskander Asanovich Taĭmanov and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Differential geometry studies geometrical objects using analytical methods. Like modern analysis itself, differential geometry originates in classical mechanics. For instance, geodesics and minimal surfaces are defined via variational principles and the curvature of a curve is easily interpreted as the acceleration with respect to the path length parameter. Modern differential geometry in its turn strongly contributed to modern physics. This book gives an introduction to the basics of differential geometry, keeping in mind the natural origin of many geometrical quantities, as well as the applications of differential geometry and its methods to other sciences. The text is divided into three parts. The first part covers the basics of curves and surfaces, while the second part is designed as an introduction to smooth manifolds and Riemannian geometry. In particular, Chapter 5 contains short introductions to hyperbolic geometry and geometrical principles of special relativity theory. Here, only a basic knowledge of algebra, calculus and ordinary differential equations is required. The third part is more advanced and introduces into matrix Lie groups and Lie algebras the representation theory of groups, symplectic and Poisson geometry, and applications of complex analysis in surface theory. The book is based on lectures the author held regularly at Novosibirsk State University. It is addressed to students as well as anyone who wants to learn the basics of differential geometry.
Fundamental Principles Of Classical Mechanics
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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 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).
Geometric Mechanics
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Author : Richard Talman
language : en
Publisher: John Wiley & Sons
Release Date : 2008-07-11
Geometric Mechanics written by Richard Talman and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-11 with Science categories.
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.
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).
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.
Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers
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Author : Hung Nguyen-Schäfer
language : en
Publisher: Springer
Release Date : 2016-08-16
Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers written by Hung Nguyen-Schäfer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-16 with Technology & Engineering categories.
This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.
Vector Methods Applied To Differential Geometry Mechanics And Potential Theory
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Author : D. E. Rutherford
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
Vector Methods Applied To Differential Geometry Mechanics And Potential Theory written by D. E. Rutherford and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
Designed to familiarize undergraduates with the methods of vector algebra and vector calculus, this text offers both a clear view of the abstract theory as well as a concise survey of the theory's applications to various branches of pure and applied mathematics. A chapter on differential geometry introduces readers to the study of this subject by the methods of vector algebra. The next section explores the many aspects of the theory of mechanics adaptable to the use of vectors, and a full discussion of the vector operator "nabla" proceeds to a treatment of potential theory and Laplace's equation. This includes applications to the theories of gravitation, hydrodynamics, and electricity. A brief chapter on four-dimensional vectors concludes the text.