Foundations Of Theoretical Mechanics I
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Foundations Of Theoretical Mechanics I
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Author : Ruggero Maria Santilli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Foundations Of Theoretical Mechanics I written by Ruggero Maria Santilli 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 2013-11-21 with Science categories.
The objective of this monograph is to present some methodological foundations of theoretical mechanics that are recommendable to graduate students prior to, or jointly with, the study of more advanced topics such as statistical mechanics, thermodynamics, and elementary particle physics. A program of this nature is inevitably centered on the methodological foundations for Newtonian systems, with particular reference to the central equations of our theories, that is, Lagrange's and Hamilton's equations. This program, realized through a study of the analytic representations in terms of Lagrange's and Hamilton's equations of generally nonconservative Newtonian systems (namely, systems with Newtonian forces not necessarily derivable from a potential function), falls within the context of the so-called Inverse Problem, and consists of three major aspects: l. The study of the necessary and sufficient conditions for the existence of a Lagrangian or Hamiltonian representation of given equations of motion with arbitrary forces; 2. The identification of the methods for the construction of a Lagrangian or Hamiltonian from given equations of motion verifying conditions 1; and 3 The analysis of the significance of the underlying methodology for other aspects of Newtonian Mechanics, e. g. , transformation theory, symmetries, and first integrals for nonconservative Newtonian systems. This first volume is devoted to the foundations of the Inverse Problem, with particular reference to aspects I and 2.
Foundations Of Theoretical Mechanics
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Author : Ruggero Maria Santilli
language : en
Publisher: Springer
Release Date : 1978
Foundations Of Theoretical Mechanics written by Ruggero Maria Santilli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Foundations Of Theoretical Mechanics Ii
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Author : Ruggero Maria Santilli
language : en
Publisher:
Release Date : 1982-12-01
Foundations Of Theoretical Mechanics Ii written by Ruggero Maria Santilli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-12-01 with categories.
Foundations Of Classical Mechanics
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Author : P. C. Deshmukh
language : en
Publisher: Cambridge University Press
Release Date : 2019-12-12
Foundations Of Classical Mechanics written by P. C. Deshmukh 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 2019-12-12 with Mathematics categories.
The book aims at speeding up undergraduates to attain interest in advanced concepts and methods in science and engineering.
Foundations Of Mechanics
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Author : Ralph Abraham
language : en
Publisher: CRC Press
Release Date : 2019-04-24
Foundations Of Mechanics written by Ralph Abraham and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-24 with Science categories.
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.
The Foundations Of Quantum Theory
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Author : Sol Wieder
language : en
Publisher: Elsevier
Release Date : 2012-12-02
The Foundations Of Quantum Theory written by Sol Wieder and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
The Foundations of Quantum Theory discusses the correspondence between the classical and quantum theories through the Poisson bracket-commutator analogy. The book is organized into three parts encompassing 12 chapters that cover topics on one-and many-particle systems and relativistic quantum mechanics and field theory. The first part of the book discusses the developments that formed the basis for the old quantum theory and the use of classical mechanics to develop the theory of quantum mechanics. This part includes considerable chapters on the formal theory of quantum mechanics and the wave mechanics in one- and three-dimension, with an emphasis on Coulomb problem or the hydrogen atom. The second part deals with the interacting particles and noninteracting indistinguishable particles and the material covered is fundamental to almost all branches of physics. The third part presents the pertinent equations used to illustrate the relativistic quantum mechanics and quantum field theory. This book is of value to undergraduate physics students and to students who have background in mechanics, electricity and magnetism, and modern physics.
Foundations Of Mechanics
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Author : Stanislaw Bazanski
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Foundations Of Mechanics written by Stanislaw Bazanski and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
In the last three decades the field of mechanics has seen spectacular progress due to the demand for applications in problems of cosmology, thermonuclear fusion, metallurgy, etc. This book provides a broad and thorough overview on the foundations of mechanics. It discusses theoretical mechanics and continuum mechanics, as well as phenomenological thermodynamics, quantum mechanics and relativistic mechanics. Each chapter presents the basic physical facts of interest without going into details and derivations and without using advanced mathematical formalism. The first part constitutes a classical exposition of Lagrange's and Hamilton's analytical mechanics on which most of the continuum theory is based. The section on continuum mechanics focuses mainly on the axiomatic foundations, with many pointers for further research in this area. Special attention is given to modern continuum thermodynamics, both for the foundations and applications. A section on quantum mechanics is also included, since the phenomenological description of various quantum phenomena is becoming of increasing importance. The work will prove indispensable to engineers wishing to keep abreast of recent theoretical advances in their field, as well as initiating and guiding future research.
New Foundations For Classical Mechanics
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Author : D. Hestenes
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-17
New Foundations For Classical Mechanics written by D. Hestenes 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 2005-12-17 with Science categories.
(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.
Variational Methods In Theoretical Mechanics
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Author : J.T. Oden
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Variational Methods In Theoretical Mechanics written by J.T. Oden 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 2012-12-06 with Technology & Engineering categories.
This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. He also gratefully acknowledge that much of our own research work on variational theory was supported by the U.S. Air Force Office of Scientific Research. He are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and pains taking job of typing the manuscript. J. T. ODEN J. N. REDDY Table of Contents PREFACE 1. INTRODUCTION 1.1 The Role of Variational Theory in Mechanics. 1 1.2 Some Historical Comments ......... . 2 1.3 Plan of Study ............... . 5 7 2. MATHEMATICAL FOUNDATIONS OF CLASSICAL VARIATIONAL THEORY 7 2.1 Introduction . . . . . . . .
New Foundations For Classical Mechanics
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Author : D. Hestenes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
New Foundations For Classical Mechanics written by D. Hestenes 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 2012-12-06 with Science categories.
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.