Foundations Of Theoretical Mechanics Ii
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Foundations Of Theoretical Mechanics Ii
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Author : Ruggero Maria Santilli
language : en
Publisher: Springer
Release Date : 2012-04-09
Foundations Of Theoretical Mechanics Ii 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 2012-04-09 with Science categories.
In the preceding volume,l I identified necessary and sufficient conditions for the existence of a representation of given Newtonian systems via a variational principle, the so-called conditions of variational self-adjointness. A primary objective of this volume is to establish that all Newtonian systems satisfying certain locality, regularity, and smoothness conditions, whether conservative or nonconservative, can be treated via conventional variational principles, Lie algebra techniques, and symplectic geometrical formulations. This volume therefore resolves a controversy on the repre sentational capabilities of conventional variational principles that has been 2 lingering in the literature for over a century, as reported in Chart 1. 3. 1. The primary results of this volume are the following. In Chapter 4,3 I prove a Theorem of Direct Universality of the Inverse Problem. It establishes the existence, via a variational principle, of a representation for all Newtonian systems of the class admitted (universality) in the coordinates and time variables of the experimenter (direct universality). The underlying analytic equations turn out to be a generalization of conventional Hamilton equations (those without external terms) which: (a) admit the most general possible action functional for first-order systems; (b) possess a Lie algebra structure in the most general possible, regular realization of the product; and (c) 1 Santilli (1978a). As was the case for Volume I, the references are listed at the end of this volume, first in chronological order and then in alphabetic order.
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 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 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.
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.
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.
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.
Foundations Of Physics
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Author : Mario Bunge
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Foundations Of Physics written by Mario Bunge 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 2013-03-13 with Science categories.
This is not an introduction to physics but an analysis of its founda tions. Indeed, the aims of this book are: (1) to analyze the form and content of some of the key ideas of physics; (2) to formulate several basic physical theories in an explicit and orderly (i. e. , axiomatic) fashion; (3) to exhibit their presuppositions and discuss some of their philosoph ical implications; (4) to discuss some of the controversial issues, and (5) to debunk certain dusty philosophical tenets that obscure the under standing of physics and hinder its progress. To the extent to which these goals are attained, the volume can serve as a companion to studies in theoretical physics aiming at deepening the understanding of the logical structure and the physical meaning of our science. In order to keep the book slender, whole fields of basic physical research had to be excluded - chiefly many-body physics, quantum field theories, and elementary particle theories. A large coverage was believed to be less important than a comparatively detailed analysis and reconstruction of three representative monuments: classical mechan ics, general relativity, and quantum mechanics, as well as their usually unrecognized presuppositions. The reader is invited to join the project and supply some of the many missing chapters - or to rewrite the present ones entirely.
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.