New Foundations For Classical Mechanics

Author : D. Hestenes
Publisher : Springer Science & Business Media
Page : 706 pages
File Size : 48,6 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306471223

Get Book

New Foundations for Classical Mechanics by D. Hestenes Pdf

(revised) This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

Author : D. Hestenes
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400948020

Get Book

New Foundations for Classical Mechanics by D. Hestenes Pdf

This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

Author : David Hestenes
Publisher : Springer
Page : 664 pages
File Size : 52,5 Mb
Release : 1986-06-30
Category : Mathematics
ISBN : UOM:39015017137434

Get Book

New Foundations for Classical Mechanics by David Hestenes Pdf

This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

Author : P. C. Deshmukh
Publisher : Cambridge University Press
Page : 591 pages
File Size : 49,9 Mb
Release : 2019-12-12
Category : Mathematics
ISBN : 9781108480567

Get Book

Foundations of Classical Mechanics by P. C. Deshmukh Pdf

The book aims at speeding up undergraduates to attain interest in advanced concepts and methods in science and engineering.

Author : David Hestenes
Publisher : Springer Science & Business Media
Page : 703 pages
File Size : 41,8 Mb
Release : 1999-09-30
Category : Language Arts & Disciplines
ISBN : 0792353021

Get Book

New Foundations for Classical Mechanics by David Hestenes Pdf

This book provides an introduction to geometric algebra as a unified language for physics and mathematics. It contains extensive applications to classical mechanics in a textbook format suitable for courses at an intermediate level. The text is supported by more than 200 diagrams to help develop geometrical and physical intuition. Besides covering the standard material for a course on the mechanics of particles and rigid bodies, the book introduces new, coordinate-free methods for rotational dynamics and orbital mechanics, developing these subjects to a level well beyond that of other textbooks. These methods have been widely applied in recent years to biomechanics and robotics, to computer vision and geometric design, to orbital mechanics in government and industrial space programs, as well as to other branches of physics. The book applies them to the major perturbations in the solar system, including the planetary perturbations of Mercury's perihelion. Geometric algebra integrates conventional vector algebra (along with its established notations) into a system with all the advantages of quaternions and spinors. Thus, it increases the power of the mathematical language of classical mechanics while bringing it closer to the language of quantum mechanics. This book systematically develops purely mathematical applications of geometric algebra useful in physics, including extensive applications to linear algebra and transformation groups. It contains sufficient material for a course on mathematical topics alone. The second edition has been expanded by nearly a hundred pages on relativistic mechanics. The treatment is unique in its exclusive use of geometric algebra and in its detailed treatment of spacetime maps, collisions, motion in uniform fields and relativistic precession. It conforms with Einstein's view that the Special Theory of Relativity is the culmination of developments in classical mechanics.

Author : Ralph Abraham
Publisher : CRC Press
Page : 849 pages
File Size : 42,7 Mb
Release : 2019-04-24
Category : Science
ISBN : 9780429689048

Get Book

Foundations Of Mechanics by Ralph Abraham Pdf

Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.

Author : John W. Arthur
Publisher : John Wiley & Sons
Page : 320 pages
File Size : 46,9 Mb
Release : 2011-09-13
Category : Science
ISBN : 9780470941638

Get Book

Understanding Geometric Algebra for Electromagnetic Theory by John W. Arthur Pdf

This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison. Professors can request a solutions manual by email: [email protected]

Author : R. Jancel
Publisher : Elsevier
Page : 440 pages
File Size : 50,9 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483186269

Get Book

Foundations of Classical and Quantum Statistical Mechanics by R. Jancel Pdf

Foundations of Classical and Quantum Statistical Mechanics details the theoretical foundation the supports the concepts in classical and quantum statistical mechanics. The title discusses the various problems set by the theoretical justification of statistical mechanics methods. The text first covers the the ergodic theory in classical statistical mechanics, and then proceeds to tackling quantum mechanical ensembles. Next, the selection discusses the the ergodic theorem in quantum statistical mechanics and probability quantum ergodic theorems. The selection also details H-theorems and kinetic equations in classical and quantum statistical mechanics. The book will be of great interest to students, researchers, and practitioners of physics, chemistry, and engineering.

Author : W. Noll
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642658174

Get Book

The Foundations of Mechanics and Thermodynamics by W. Noll Pdf

German scholars, against odds now not only forgotten but also hard to imagine, were striving to revivify the life of the mind which the mental and physical barbarity preached and practised by the -isms and -acies of 1933-1946 had all but eradicated. Thinking that among the disciples of these elders, restorers rather than progressives, I might find a student or two who would wish to master new mathematics but grasp it and use it with the wholeness of earlier times, in 1952 I wrote to Mr. HAMEL, one of the few then remaining mathematicians from the classical mould, to ask him to name some young men fit to study for the doc torate in The Graduate Institute for Applied Mathematics at Indiana University, flourishing at that time though soon to be destroyed by the jealous ambition of the local, stereotyped pure. Having just retired from the Technische Universitat in Charlottenburg, he passed my inquiry on to Mr. SZABO, in whose institute there NOLL was then an assistant. Although Mr.

Author : V.I. Arnol'd
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 40,6 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9781475720631

Get Book

Mathematical Methods of Classical Mechanics by V.I. Arnol'd Pdf

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.

Author : Antonio Romano,Addolorata Marasco
Publisher : Springer
Page : 644 pages
File Size : 43,8 Mb
Release : 2018-05-29
Category : Science
ISBN : 9783319775951

Get Book

Classical Mechanics with Mathematica® by Antonio Romano,Addolorata Marasco Pdf

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the authors from over 30 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Hamilton—while also painting a clear picture of the most modern developments. The text is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others. This new edition has been completely revised and updated and now includes almost 200 exercises, as well as new chapters on celestial mechanics, one-dimensional continuous systems, and variational calculus with applications. Several Mathematica® notebooks are available to download that will further aid students in their understanding of some of the more difficult material. Unique in its scope of coverage and method of approach, Classical Mechanics with Mathematica® will be useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.

Author : Michael Spivak
Publisher : Unknown
Page : 733 pages
File Size : 40,9 Mb
Release : 2010
Category : Mechanics
ISBN : 0914098322

Get Book

Physics for Mathematicians by Michael Spivak Pdf

Author : D.Ya. Petrina,V.I. Gerasimenko,P V Malyshev
Publisher : CRC Press
Page : 352 pages
File Size : 48,7 Mb
Release : 2002-04-11
Category : Science
ISBN : 0415273544

Get Book

Mathematical Foundations of Classical Statistical Mechanics by D.Ya. Petrina,V.I. Gerasimenko,P V Malyshev Pdf

This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov equations for the sequences of correlation functions in the thermodynamic limit. This is the first detailed investigation of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in the cases of both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. A comprehensive survey of results is also included; it concerns the properties of correlation functions for infinite systems and the corresponding equations. For this new edition, the authors have made changes to reflect the development of theory in the last ten years. They have also simplified certain sections, presenting them more systematically, and greatly increased the number of references. The book is aimed at theoretical physicists and mathematicians and will also be of use to students and postgraduate students in the field.

Author : Alfred Lande
Publisher : Cambridge University Press
Page : 185 pages
File Size : 44,5 Mb
Release : 2015-12-03
Category : Science
ISBN : 9781107593541

Get Book

New Foundations of Quantum Mechanics by Alfred Lande Pdf

Originally published in 1965, the aim of this book was to challenge the dualistic view of physics, that is, the assumption that beams of electrons consist of discrete particles and of waves. Lande argues that this dualistic view is unnecessary, not only on methodological grounds but also from the standpoint of physics. Lande sets out to point out that there are faults in the purely physical arguments, which have led to the dualistic doctrine and shows that by making use of the quantum rule for the exchange of linear momentum, established by W. Duane in 1923, wave-like phenomena can be fully explained on a unitary particle theory of matter. Chapters cover a variety of subjects and range from 'Dualism versus quantum mechanics' to the 'Origin of the quantum rules'. Appendices are included for reference. This book will be of value to students and scholars of the history of physics.

Author : David Hestenes,Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 47,6 Mb
Release : 1984
Category : Mathematics
ISBN : 9027725616

Get Book

Clifford Algebra to Geometric Calculus by David Hestenes,Garret Sobczyk Pdf

Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.